Volume and Surface Area of Solids | Mathematics (Maths) Class 8 PDF Download

 Page 1


Q u e s t i o n : 1
Find the volume, lateral surface area and the total surface area of the cuboid whose dimensions are:
i
length = 22 cm, breadth = 12 cm and height = 7.5 cm
ii
length = 15 m, breadth = 6 m and height = 9 dm
iii
length = 24 m, breadth = 25 cm and height = 6 m
iv
length = 48 cm, breadth = 6 dm and height = 1 m
S o l u t i o n :
Volume of a cuboid = (Length ×Breadth ×Height)
 cubic units
Total surface area = 2(lb +bh +lh)
 sq units
Lateral surface area = [2(l +b)×h]
 sq units
i
Length = 22 cm, breadth = 12 cm, height = 7.5 cm
Volume = (Length ×Breadth ×Height)
 = 22 ×12 ×7. 5 = 1980 cm
3
Total surface area = 2(lb +bh +lh)
= 2[(22 ×12)+(22 ×7. 5)+(12 ×7. 5)] = 2[264 +165 +90] = 1038 cm
2
Lateral surface area = [2(l +b)×h]
= 2(22 +12)×7. 5 = 510 cm
2
ii
Length = 15 m, breadth = 6 m, height = 9 dm = 0.9 m
Volume = (Length ×Breadth ×Height)
 = 15 ×6 ×0. 9 = 81 m
3
Total surface area = 2(lb +bh +lh)
 = 2[(15 ×6)+(15 ×0. 9)+(6 ×0. 9)] = 2[90 +13. 5 +5. 4] = 217. 8 m
2
Lateral surface area = [2(l +b)×h]
= 2(15 +6)×0. 9 = 37. 8 m
2
iii
Length = 24 m, breadth = 25 cm = 0.25 m, height = 6 m
Volume = (Length ×Breadth ×Height)
 = 24 ×0. 25 ×6 = 36 m
3
Total surface area = 2(lb +bh +lh)
 = 2[(24 ×0. 25)+(24 ×6)+(0. 25 ×6)] = 2[6 +144 +1. 5] = 303 m
2
Lateral surface area = [2(l +b)×h]
= 2(24 +0. 25)×6 = 291 m
2
iv
Length = 48 cm = 0.48 m, breadth = 6 dm = 0.6 m, height = 1 m
Volume = (Length ×Breadth ×Height)
 = 0. 48 ×0. 6 ×1 = 0. 288 m
3
Total surface area = 2(lb +bh +lh)
= 2[(0. 48 ×0. 6)+(0. 48 ×1)+(0. 6 ×1)] = 2[0. 288 +0. 48 +0. 6] = 2. 736 m
2
Lateral surface area = [2(l +b)×h]
= 2(0. 48 +0. 6)×1 = 2. 16 m
2
Q u e s t i o n : 2
The dimensions of a rectangular water tank are 2 m 75 cm by 1 m 80 cm by 1 m 40 cm. How many litres of water does it hold when filled to the brim?
S o l u t i o n :
 1 m = 100 cm
Therefore, dimensions of the tank are:
2 m 75 cm × 1 m 80 cm × 1 m 40 cm = 275 cm × 180 cm × 140 cm
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Page 2


Q u e s t i o n : 1
Find the volume, lateral surface area and the total surface area of the cuboid whose dimensions are:
i
length = 22 cm, breadth = 12 cm and height = 7.5 cm
ii
length = 15 m, breadth = 6 m and height = 9 dm
iii
length = 24 m, breadth = 25 cm and height = 6 m
iv
length = 48 cm, breadth = 6 dm and height = 1 m
S o l u t i o n :
Volume of a cuboid = (Length ×Breadth ×Height)
 cubic units
Total surface area = 2(lb +bh +lh)
 sq units
Lateral surface area = [2(l +b)×h]
 sq units
i
Length = 22 cm, breadth = 12 cm, height = 7.5 cm
Volume = (Length ×Breadth ×Height)
 = 22 ×12 ×7. 5 = 1980 cm
3
Total surface area = 2(lb +bh +lh)
= 2[(22 ×12)+(22 ×7. 5)+(12 ×7. 5)] = 2[264 +165 +90] = 1038 cm
2
Lateral surface area = [2(l +b)×h]
= 2(22 +12)×7. 5 = 510 cm
2
ii
Length = 15 m, breadth = 6 m, height = 9 dm = 0.9 m
Volume = (Length ×Breadth ×Height)
 = 15 ×6 ×0. 9 = 81 m
3
Total surface area = 2(lb +bh +lh)
 = 2[(15 ×6)+(15 ×0. 9)+(6 ×0. 9)] = 2[90 +13. 5 +5. 4] = 217. 8 m
2
Lateral surface area = [2(l +b)×h]
= 2(15 +6)×0. 9 = 37. 8 m
2
iii
Length = 24 m, breadth = 25 cm = 0.25 m, height = 6 m
Volume = (Length ×Breadth ×Height)
 = 24 ×0. 25 ×6 = 36 m
3
Total surface area = 2(lb +bh +lh)
 = 2[(24 ×0. 25)+(24 ×6)+(0. 25 ×6)] = 2[6 +144 +1. 5] = 303 m
2
Lateral surface area = [2(l +b)×h]
= 2(24 +0. 25)×6 = 291 m
2
iv
Length = 48 cm = 0.48 m, breadth = 6 dm = 0.6 m, height = 1 m
Volume = (Length ×Breadth ×Height)
 = 0. 48 ×0. 6 ×1 = 0. 288 m
3
Total surface area = 2(lb +bh +lh)
= 2[(0. 48 ×0. 6)+(0. 48 ×1)+(0. 6 ×1)] = 2[0. 288 +0. 48 +0. 6] = 2. 736 m
2
Lateral surface area = [2(l +b)×h]
= 2(0. 48 +0. 6)×1 = 2. 16 m
2
Q u e s t i o n : 2
The dimensions of a rectangular water tank are 2 m 75 cm by 1 m 80 cm by 1 m 40 cm. How many litres of water does it hold when filled to the brim?
S o l u t i o n :
 1 m = 100 cm
Therefore, dimensions of the tank are:
2 m 75 cm × 1 m 80 cm × 1 m 40 cm = 275 cm × 180 cm × 140 cm
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( )
? Volume =  Length × Breadth × Height = 275 ×180 ×140 = 6930000 cm
3
Also, 1000cm
3
= 1L
? Volume =
6930000
1000
= 6930 L
Q u e s t i o n : 3
A solid rectangular piece of iron measures 1.05 m × 70 cm × 1.5 cm. Find the weight of this piece in kilograms if 1 cm
3
 of iron weighs 8 grams.
S o l u t i o n :
1m = 100cm
? Dimensions of the iron piece = 105 cm ×70 cm ×1. 5 cm
Total volume of the piece of iron = 105 ×70 ×1. 5 = 11025 cm
3
1 cm
3
 measures 8 gms.
?Weight of the piece = 11025 × 8 = 88200 g =
88200
1000
 = 88. 2 kg                      (because 1 kg = 1000 g)
Q u e s t i o n : 4
The area of a courtyard is 3750 m
2
. Find the cost of covering it with gravel to a height of 1 cm if the gravel costs Rs 6.40 per cubic metre.
S o l u t i o n :
1 cm = 0. 01 m
Volume of the gravel used = Area × Height = 3750 × 0. 01 = 37. 5 m
3
Cost of the gravel is Rs 6.40 per cubic meter.
? Total cost = (37. 5 ×6. 4) = 
Rs 240
Q u e s t i o n : 5
How many persons can be accommodated in a hall of length 16 m. breadth 12.5 m and height 4.5 m, assuming that 3.6 m
3
 of air is required for each person?
S o l u t i o n :
Total volume of the hall = 16 ×12. 5 ×4. 5 = 900 m
3
It is given that 3. 6 m
3
 of air is required for each person.
The total number of persons that can be accommodated in that hall =
Total volume
Volume required by each person
= 
900
3.6
= 250 people
 
Q u e s t i o n : 6
A cardboard box is 1.2 m long, 72 cm wide and 54 cm high. How many bars of soap can be put into it if each bar measures 6 cm × 4.5 cm × 4 cm?
S o l u t i o n :
Volume of the cardboard box = 120 ×72 ×54 = 466560 cm
3
Volume of each bar of soap = 6 ×4. 5 ×4 = 108 cm
3
Total number of bars of soap that can be accommodated in that box =
Volume of the box
Volume of each soap
=
466560
108
= 4320
 bars
Q u e s t i o n : 7
The size of a matchbox is 4 cm × 2.5 cm × 1.5 cm. What is the volume of a packet containing 144 matchboxes? How many such packets can be placed in
a carton of size 1.5 m × 84 cm × 60 cm?
S o l u t i o n :
Volume occupied by a single matchbox = 4 ×2. 5 ×1. 5 = 15 cm
3
Volume of a packet containing 144 matchboxes = 15 ×144 = 2160 cm
3
Volume of the carton = 150 ×84 ×60 = 756000 cm
3
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Page 3


Q u e s t i o n : 1
Find the volume, lateral surface area and the total surface area of the cuboid whose dimensions are:
i
length = 22 cm, breadth = 12 cm and height = 7.5 cm
ii
length = 15 m, breadth = 6 m and height = 9 dm
iii
length = 24 m, breadth = 25 cm and height = 6 m
iv
length = 48 cm, breadth = 6 dm and height = 1 m
S o l u t i o n :
Volume of a cuboid = (Length ×Breadth ×Height)
 cubic units
Total surface area = 2(lb +bh +lh)
 sq units
Lateral surface area = [2(l +b)×h]
 sq units
i
Length = 22 cm, breadth = 12 cm, height = 7.5 cm
Volume = (Length ×Breadth ×Height)
 = 22 ×12 ×7. 5 = 1980 cm
3
Total surface area = 2(lb +bh +lh)
= 2[(22 ×12)+(22 ×7. 5)+(12 ×7. 5)] = 2[264 +165 +90] = 1038 cm
2
Lateral surface area = [2(l +b)×h]
= 2(22 +12)×7. 5 = 510 cm
2
ii
Length = 15 m, breadth = 6 m, height = 9 dm = 0.9 m
Volume = (Length ×Breadth ×Height)
 = 15 ×6 ×0. 9 = 81 m
3
Total surface area = 2(lb +bh +lh)
 = 2[(15 ×6)+(15 ×0. 9)+(6 ×0. 9)] = 2[90 +13. 5 +5. 4] = 217. 8 m
2
Lateral surface area = [2(l +b)×h]
= 2(15 +6)×0. 9 = 37. 8 m
2
iii
Length = 24 m, breadth = 25 cm = 0.25 m, height = 6 m
Volume = (Length ×Breadth ×Height)
 = 24 ×0. 25 ×6 = 36 m
3
Total surface area = 2(lb +bh +lh)
 = 2[(24 ×0. 25)+(24 ×6)+(0. 25 ×6)] = 2[6 +144 +1. 5] = 303 m
2
Lateral surface area = [2(l +b)×h]
= 2(24 +0. 25)×6 = 291 m
2
iv
Length = 48 cm = 0.48 m, breadth = 6 dm = 0.6 m, height = 1 m
Volume = (Length ×Breadth ×Height)
 = 0. 48 ×0. 6 ×1 = 0. 288 m
3
Total surface area = 2(lb +bh +lh)
= 2[(0. 48 ×0. 6)+(0. 48 ×1)+(0. 6 ×1)] = 2[0. 288 +0. 48 +0. 6] = 2. 736 m
2
Lateral surface area = [2(l +b)×h]
= 2(0. 48 +0. 6)×1 = 2. 16 m
2
Q u e s t i o n : 2
The dimensions of a rectangular water tank are 2 m 75 cm by 1 m 80 cm by 1 m 40 cm. How many litres of water does it hold when filled to the brim?
S o l u t i o n :
 1 m = 100 cm
Therefore, dimensions of the tank are:
2 m 75 cm × 1 m 80 cm × 1 m 40 cm = 275 cm × 180 cm × 140 cm
( )
( )
( )
( )
? Volume =  Length × Breadth × Height = 275 ×180 ×140 = 6930000 cm
3
Also, 1000cm
3
= 1L
? Volume =
6930000
1000
= 6930 L
Q u e s t i o n : 3
A solid rectangular piece of iron measures 1.05 m × 70 cm × 1.5 cm. Find the weight of this piece in kilograms if 1 cm
3
 of iron weighs 8 grams.
S o l u t i o n :
1m = 100cm
? Dimensions of the iron piece = 105 cm ×70 cm ×1. 5 cm
Total volume of the piece of iron = 105 ×70 ×1. 5 = 11025 cm
3
1 cm
3
 measures 8 gms.
?Weight of the piece = 11025 × 8 = 88200 g =
88200
1000
 = 88. 2 kg                      (because 1 kg = 1000 g)
Q u e s t i o n : 4
The area of a courtyard is 3750 m
2
. Find the cost of covering it with gravel to a height of 1 cm if the gravel costs Rs 6.40 per cubic metre.
S o l u t i o n :
1 cm = 0. 01 m
Volume of the gravel used = Area × Height = 3750 × 0. 01 = 37. 5 m
3
Cost of the gravel is Rs 6.40 per cubic meter.
? Total cost = (37. 5 ×6. 4) = 
Rs 240
Q u e s t i o n : 5
How many persons can be accommodated in a hall of length 16 m. breadth 12.5 m and height 4.5 m, assuming that 3.6 m
3
 of air is required for each person?
S o l u t i o n :
Total volume of the hall = 16 ×12. 5 ×4. 5 = 900 m
3
It is given that 3. 6 m
3
 of air is required for each person.
The total number of persons that can be accommodated in that hall =
Total volume
Volume required by each person
= 
900
3.6
= 250 people
 
Q u e s t i o n : 6
A cardboard box is 1.2 m long, 72 cm wide and 54 cm high. How many bars of soap can be put into it if each bar measures 6 cm × 4.5 cm × 4 cm?
S o l u t i o n :
Volume of the cardboard box = 120 ×72 ×54 = 466560 cm
3
Volume of each bar of soap = 6 ×4. 5 ×4 = 108 cm
3
Total number of bars of soap that can be accommodated in that box =
Volume of the box
Volume of each soap
=
466560
108
= 4320
 bars
Q u e s t i o n : 7
The size of a matchbox is 4 cm × 2.5 cm × 1.5 cm. What is the volume of a packet containing 144 matchboxes? How many such packets can be placed in
a carton of size 1.5 m × 84 cm × 60 cm?
S o l u t i o n :
Volume occupied by a single matchbox = 4 ×2. 5 ×1. 5 = 15 cm
3
Volume of a packet containing 144 matchboxes = 15 ×144 = 2160 cm
3
Volume of the carton = 150 ×84 ×60 = 756000 cm
3
( )
( )
( )
( )
( )
( )
( )
( )
Total number of packets is a carton =
Volume of the carton
Volume of a packet 
= 
75600
2160
= 350
 packets
Q u e s t i o n : 8
How many planks of size 2 m × 25 cm × 8 cm can be prepared from a wooden block 5 m long, 70 cm broad and 32 cm thick, assuming that there is no
wastage?
S o l u t i o n :
Total volume of the block = 500 ×70 ×32 = 1120000 cm
3
 
Total volume of each plank = 200 ×25 ×8 = 40000 cm
3
= 200 ×25 ×8 = 40000 cm
3
? Total number of planks that can be made =
Total volume of the block
Volume of each plank
 = 
1120000
40000
= 28
 planks
Q u e s t i o n : 9
How many bricks, each of size 25 cm × 13.5 cm × 6 cm, will be required to build a wall 8 m long, 5.4 m high and 33 cm thick?
S o l u t i o n :
Volume of the brick = 25 ×13. 5 ×6 = 2025 cm
3
Volume of the wall = 800 ×540 ×33 = 14256000 cm
3
Total number of bricks =
Volume of the wall
Volume of each brick
=
14256000
2025
= 7040
 bricks  
Q u e s t i o n : 1 0
A wall 15 m long, 30 cm wide and 4 m high is made of bricks, each measuring 22 cm × 12.5 cm × 7.5 cm. If 
1
12
of the total volume of the wall consists of mortar, how many bricks are there in the wall?
S o l u t i o n :
Volume of the wall = 1500 ×30 ×400 = 18000000 cm
3
Total quantity of mortar =
1
12
×18000000 = 1500000 cm
3
? Volume of the bricks = 18000000 -1500000 = 16500000 cm
3
Volume of a single brick = 22 ×12. 5 ×7. 5 = 2062. 5 cm
3
? Total number of bricks =
Total volume of the bricks
Volume of a single brick
=
16500000
2062.5
= 8000
 bricks
Q u e s t i o n : 1 1
Find the capacity of a rectangular cistern in litres whose dimensions are 11.2 m × 6 m × 5.8 m. Find the area of the iron sheet required to make the cistern.
S o l u t i o n :
Volume of the cistern = 11. 2 ×6 ×5. 8 = 389. 76 m
3
= 389. 76 ×1000 = 389760
 litres
Area of the iron sheet required to make this cistern = Total surface area of the cistern
= 2 11. 2 ×6 +11. 2 ×5. 8 +6 ×5. 8 = 2 67. 2 +64. 96 +34. 8 = 333. 92 cm
2
Q u e s t i o n : 1 2
The volume of a block of gold is 0.5 m
3
. If it is hammered into a sheet to cover an area of 1 hectare, find the thickness of the sheet.
S o l u t i o n :
Volume of the block = 0. 5 m
3
We know:
 1 hectare = 10000 m
2
Thickness =
Volume
Area
=
0.5
10000
= 0. 00005 m = 0. 005 cm = 0. 05 mm
Q u e s t i o n : 1 3
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Page 4


Q u e s t i o n : 1
Find the volume, lateral surface area and the total surface area of the cuboid whose dimensions are:
i
length = 22 cm, breadth = 12 cm and height = 7.5 cm
ii
length = 15 m, breadth = 6 m and height = 9 dm
iii
length = 24 m, breadth = 25 cm and height = 6 m
iv
length = 48 cm, breadth = 6 dm and height = 1 m
S o l u t i o n :
Volume of a cuboid = (Length ×Breadth ×Height)
 cubic units
Total surface area = 2(lb +bh +lh)
 sq units
Lateral surface area = [2(l +b)×h]
 sq units
i
Length = 22 cm, breadth = 12 cm, height = 7.5 cm
Volume = (Length ×Breadth ×Height)
 = 22 ×12 ×7. 5 = 1980 cm
3
Total surface area = 2(lb +bh +lh)
= 2[(22 ×12)+(22 ×7. 5)+(12 ×7. 5)] = 2[264 +165 +90] = 1038 cm
2
Lateral surface area = [2(l +b)×h]
= 2(22 +12)×7. 5 = 510 cm
2
ii
Length = 15 m, breadth = 6 m, height = 9 dm = 0.9 m
Volume = (Length ×Breadth ×Height)
 = 15 ×6 ×0. 9 = 81 m
3
Total surface area = 2(lb +bh +lh)
 = 2[(15 ×6)+(15 ×0. 9)+(6 ×0. 9)] = 2[90 +13. 5 +5. 4] = 217. 8 m
2
Lateral surface area = [2(l +b)×h]
= 2(15 +6)×0. 9 = 37. 8 m
2
iii
Length = 24 m, breadth = 25 cm = 0.25 m, height = 6 m
Volume = (Length ×Breadth ×Height)
 = 24 ×0. 25 ×6 = 36 m
3
Total surface area = 2(lb +bh +lh)
 = 2[(24 ×0. 25)+(24 ×6)+(0. 25 ×6)] = 2[6 +144 +1. 5] = 303 m
2
Lateral surface area = [2(l +b)×h]
= 2(24 +0. 25)×6 = 291 m
2
iv
Length = 48 cm = 0.48 m, breadth = 6 dm = 0.6 m, height = 1 m
Volume = (Length ×Breadth ×Height)
 = 0. 48 ×0. 6 ×1 = 0. 288 m
3
Total surface area = 2(lb +bh +lh)
= 2[(0. 48 ×0. 6)+(0. 48 ×1)+(0. 6 ×1)] = 2[0. 288 +0. 48 +0. 6] = 2. 736 m
2
Lateral surface area = [2(l +b)×h]
= 2(0. 48 +0. 6)×1 = 2. 16 m
2
Q u e s t i o n : 2
The dimensions of a rectangular water tank are 2 m 75 cm by 1 m 80 cm by 1 m 40 cm. How many litres of water does it hold when filled to the brim?
S o l u t i o n :
 1 m = 100 cm
Therefore, dimensions of the tank are:
2 m 75 cm × 1 m 80 cm × 1 m 40 cm = 275 cm × 180 cm × 140 cm
( )
( )
( )
( )
? Volume =  Length × Breadth × Height = 275 ×180 ×140 = 6930000 cm
3
Also, 1000cm
3
= 1L
? Volume =
6930000
1000
= 6930 L
Q u e s t i o n : 3
A solid rectangular piece of iron measures 1.05 m × 70 cm × 1.5 cm. Find the weight of this piece in kilograms if 1 cm
3
 of iron weighs 8 grams.
S o l u t i o n :
1m = 100cm
? Dimensions of the iron piece = 105 cm ×70 cm ×1. 5 cm
Total volume of the piece of iron = 105 ×70 ×1. 5 = 11025 cm
3
1 cm
3
 measures 8 gms.
?Weight of the piece = 11025 × 8 = 88200 g =
88200
1000
 = 88. 2 kg                      (because 1 kg = 1000 g)
Q u e s t i o n : 4
The area of a courtyard is 3750 m
2
. Find the cost of covering it with gravel to a height of 1 cm if the gravel costs Rs 6.40 per cubic metre.
S o l u t i o n :
1 cm = 0. 01 m
Volume of the gravel used = Area × Height = 3750 × 0. 01 = 37. 5 m
3
Cost of the gravel is Rs 6.40 per cubic meter.
? Total cost = (37. 5 ×6. 4) = 
Rs 240
Q u e s t i o n : 5
How many persons can be accommodated in a hall of length 16 m. breadth 12.5 m and height 4.5 m, assuming that 3.6 m
3
 of air is required for each person?
S o l u t i o n :
Total volume of the hall = 16 ×12. 5 ×4. 5 = 900 m
3
It is given that 3. 6 m
3
 of air is required for each person.
The total number of persons that can be accommodated in that hall =
Total volume
Volume required by each person
= 
900
3.6
= 250 people
 
Q u e s t i o n : 6
A cardboard box is 1.2 m long, 72 cm wide and 54 cm high. How many bars of soap can be put into it if each bar measures 6 cm × 4.5 cm × 4 cm?
S o l u t i o n :
Volume of the cardboard box = 120 ×72 ×54 = 466560 cm
3
Volume of each bar of soap = 6 ×4. 5 ×4 = 108 cm
3
Total number of bars of soap that can be accommodated in that box =
Volume of the box
Volume of each soap
=
466560
108
= 4320
 bars
Q u e s t i o n : 7
The size of a matchbox is 4 cm × 2.5 cm × 1.5 cm. What is the volume of a packet containing 144 matchboxes? How many such packets can be placed in
a carton of size 1.5 m × 84 cm × 60 cm?
S o l u t i o n :
Volume occupied by a single matchbox = 4 ×2. 5 ×1. 5 = 15 cm
3
Volume of a packet containing 144 matchboxes = 15 ×144 = 2160 cm
3
Volume of the carton = 150 ×84 ×60 = 756000 cm
3
( )
( )
( )
( )
( )
( )
( )
( )
Total number of packets is a carton =
Volume of the carton
Volume of a packet 
= 
75600
2160
= 350
 packets
Q u e s t i o n : 8
How many planks of size 2 m × 25 cm × 8 cm can be prepared from a wooden block 5 m long, 70 cm broad and 32 cm thick, assuming that there is no
wastage?
S o l u t i o n :
Total volume of the block = 500 ×70 ×32 = 1120000 cm
3
 
Total volume of each plank = 200 ×25 ×8 = 40000 cm
3
= 200 ×25 ×8 = 40000 cm
3
? Total number of planks that can be made =
Total volume of the block
Volume of each plank
 = 
1120000
40000
= 28
 planks
Q u e s t i o n : 9
How many bricks, each of size 25 cm × 13.5 cm × 6 cm, will be required to build a wall 8 m long, 5.4 m high and 33 cm thick?
S o l u t i o n :
Volume of the brick = 25 ×13. 5 ×6 = 2025 cm
3
Volume of the wall = 800 ×540 ×33 = 14256000 cm
3
Total number of bricks =
Volume of the wall
Volume of each brick
=
14256000
2025
= 7040
 bricks  
Q u e s t i o n : 1 0
A wall 15 m long, 30 cm wide and 4 m high is made of bricks, each measuring 22 cm × 12.5 cm × 7.5 cm. If 
1
12
of the total volume of the wall consists of mortar, how many bricks are there in the wall?
S o l u t i o n :
Volume of the wall = 1500 ×30 ×400 = 18000000 cm
3
Total quantity of mortar =
1
12
×18000000 = 1500000 cm
3
? Volume of the bricks = 18000000 -1500000 = 16500000 cm
3
Volume of a single brick = 22 ×12. 5 ×7. 5 = 2062. 5 cm
3
? Total number of bricks =
Total volume of the bricks
Volume of a single brick
=
16500000
2062.5
= 8000
 bricks
Q u e s t i o n : 1 1
Find the capacity of a rectangular cistern in litres whose dimensions are 11.2 m × 6 m × 5.8 m. Find the area of the iron sheet required to make the cistern.
S o l u t i o n :
Volume of the cistern = 11. 2 ×6 ×5. 8 = 389. 76 m
3
= 389. 76 ×1000 = 389760
 litres
Area of the iron sheet required to make this cistern = Total surface area of the cistern
= 2 11. 2 ×6 +11. 2 ×5. 8 +6 ×5. 8 = 2 67. 2 +64. 96 +34. 8 = 333. 92 cm
2
Q u e s t i o n : 1 2
The volume of a block of gold is 0.5 m
3
. If it is hammered into a sheet to cover an area of 1 hectare, find the thickness of the sheet.
S o l u t i o n :
Volume of the block = 0. 5 m
3
We know:
 1 hectare = 10000 m
2
Thickness =
Volume
Area
=
0.5
10000
= 0. 00005 m = 0. 005 cm = 0. 05 mm
Q u e s t i o n : 1 3
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( ) ( )
The rainfall recorded on a certain day was 5 cm. Find the volume of water that fell on a 2-hectare field.
S o l u t i o n :
Rainfall recorded = 5 cm = 0.05 m
Area of the field = 2 hectare =  2 ×10000 m
2 
 = 20000 m
2
Total rain over the field = Area of the field × Height of the field = 0. 05 × 20000 = 1000 m
3
Q u e s t i o n : 1 4
A river 2 m deep and 45 m wide is flowing at the rate of 3 km/h. Find the quantity of water that runs into the sea per minute.
S o l u t i o n :
Area of the cross-section of river = 45 ×2 = 90 m
2
Rate of flow = 3
 km
hr
=
3×1000
60
= 50 
m
min
Volume of water flowing through the cross-section in one minute = 90 ×50 = 4500 m
3
 per minute
Q u e s t i o n : 1 5
A pit 5 m long and 3.5 m wide is dug to a certain depth. If the volume of earth taken out of it is 14 m
3
, what is the depth of the pit?
S o l u t i o n :
Let the depth of the pit be d m.
Volume = Length × width × depth = 5 m × 3. 5 m × d m
But,
Given volume = 14 m
3
? Depth = d =
volume
length × width
=
14
5×3.5
= 0. 8 m
= 80 cm
Q u e s t i o n : 1 6
A rectangular water tank is 90 cm wide and 40 cm deep. If it can contain 576 litres of water, what is its length?
S o l u t i o n :
Capacity of the water tank = 576 litres = 0. 576 m
3
Width = 90 cm = 0.9 m
Depth = 40 cm = 0.4 m
Length = =
capacity
width×depth
=
0.576
0.9×0.4
= 1. 600 m
Q u e s t i o n : 1 7
A beam of wood is 5 m long and 36 cm thick. It is made of 1.35 m
3
 of wood. What is the width of the beam?
S o l u t i o n :
Volume of the beam = 1. 35 m
3
Length = 5 m
Thickness = 36 cm = 0.36 m
Width = =
volume
thickness×length
=
1.35
5×0.36
= 0. 75 m = 75 cm
Q u e s t i o n : 1 8
The volume of a room is 378 m
3
 and the area of its floor is 84 m
2
. Find the height of the room.
S o l u t i o n :
Volume = height × area
Given:
 Volume  = 378 m
3
Area = 84 m
2
? Height =
volume
area
=
378
84
= 4. 5 m
Q u e s t i o n : 1 9
A swimming pool is 260 m long and 140 m wide. If 54600 cubic metres of water is pumped into it, find the height of the water level in it.
S o l u t i o n :
Length of the pool = 260 m
Width of the pool = 140 m
Page 5


Q u e s t i o n : 1
Find the volume, lateral surface area and the total surface area of the cuboid whose dimensions are:
i
length = 22 cm, breadth = 12 cm and height = 7.5 cm
ii
length = 15 m, breadth = 6 m and height = 9 dm
iii
length = 24 m, breadth = 25 cm and height = 6 m
iv
length = 48 cm, breadth = 6 dm and height = 1 m
S o l u t i o n :
Volume of a cuboid = (Length ×Breadth ×Height)
 cubic units
Total surface area = 2(lb +bh +lh)
 sq units
Lateral surface area = [2(l +b)×h]
 sq units
i
Length = 22 cm, breadth = 12 cm, height = 7.5 cm
Volume = (Length ×Breadth ×Height)
 = 22 ×12 ×7. 5 = 1980 cm
3
Total surface area = 2(lb +bh +lh)
= 2[(22 ×12)+(22 ×7. 5)+(12 ×7. 5)] = 2[264 +165 +90] = 1038 cm
2
Lateral surface area = [2(l +b)×h]
= 2(22 +12)×7. 5 = 510 cm
2
ii
Length = 15 m, breadth = 6 m, height = 9 dm = 0.9 m
Volume = (Length ×Breadth ×Height)
 = 15 ×6 ×0. 9 = 81 m
3
Total surface area = 2(lb +bh +lh)
 = 2[(15 ×6)+(15 ×0. 9)+(6 ×0. 9)] = 2[90 +13. 5 +5. 4] = 217. 8 m
2
Lateral surface area = [2(l +b)×h]
= 2(15 +6)×0. 9 = 37. 8 m
2
iii
Length = 24 m, breadth = 25 cm = 0.25 m, height = 6 m
Volume = (Length ×Breadth ×Height)
 = 24 ×0. 25 ×6 = 36 m
3
Total surface area = 2(lb +bh +lh)
 = 2[(24 ×0. 25)+(24 ×6)+(0. 25 ×6)] = 2[6 +144 +1. 5] = 303 m
2
Lateral surface area = [2(l +b)×h]
= 2(24 +0. 25)×6 = 291 m
2
iv
Length = 48 cm = 0.48 m, breadth = 6 dm = 0.6 m, height = 1 m
Volume = (Length ×Breadth ×Height)
 = 0. 48 ×0. 6 ×1 = 0. 288 m
3
Total surface area = 2(lb +bh +lh)
= 2[(0. 48 ×0. 6)+(0. 48 ×1)+(0. 6 ×1)] = 2[0. 288 +0. 48 +0. 6] = 2. 736 m
2
Lateral surface area = [2(l +b)×h]
= 2(0. 48 +0. 6)×1 = 2. 16 m
2
Q u e s t i o n : 2
The dimensions of a rectangular water tank are 2 m 75 cm by 1 m 80 cm by 1 m 40 cm. How many litres of water does it hold when filled to the brim?
S o l u t i o n :
 1 m = 100 cm
Therefore, dimensions of the tank are:
2 m 75 cm × 1 m 80 cm × 1 m 40 cm = 275 cm × 180 cm × 140 cm
( )
( )
( )
( )
? Volume =  Length × Breadth × Height = 275 ×180 ×140 = 6930000 cm
3
Also, 1000cm
3
= 1L
? Volume =
6930000
1000
= 6930 L
Q u e s t i o n : 3
A solid rectangular piece of iron measures 1.05 m × 70 cm × 1.5 cm. Find the weight of this piece in kilograms if 1 cm
3
 of iron weighs 8 grams.
S o l u t i o n :
1m = 100cm
? Dimensions of the iron piece = 105 cm ×70 cm ×1. 5 cm
Total volume of the piece of iron = 105 ×70 ×1. 5 = 11025 cm
3
1 cm
3
 measures 8 gms.
?Weight of the piece = 11025 × 8 = 88200 g =
88200
1000
 = 88. 2 kg                      (because 1 kg = 1000 g)
Q u e s t i o n : 4
The area of a courtyard is 3750 m
2
. Find the cost of covering it with gravel to a height of 1 cm if the gravel costs Rs 6.40 per cubic metre.
S o l u t i o n :
1 cm = 0. 01 m
Volume of the gravel used = Area × Height = 3750 × 0. 01 = 37. 5 m
3
Cost of the gravel is Rs 6.40 per cubic meter.
? Total cost = (37. 5 ×6. 4) = 
Rs 240
Q u e s t i o n : 5
How many persons can be accommodated in a hall of length 16 m. breadth 12.5 m and height 4.5 m, assuming that 3.6 m
3
 of air is required for each person?
S o l u t i o n :
Total volume of the hall = 16 ×12. 5 ×4. 5 = 900 m
3
It is given that 3. 6 m
3
 of air is required for each person.
The total number of persons that can be accommodated in that hall =
Total volume
Volume required by each person
= 
900
3.6
= 250 people
 
Q u e s t i o n : 6
A cardboard box is 1.2 m long, 72 cm wide and 54 cm high. How many bars of soap can be put into it if each bar measures 6 cm × 4.5 cm × 4 cm?
S o l u t i o n :
Volume of the cardboard box = 120 ×72 ×54 = 466560 cm
3
Volume of each bar of soap = 6 ×4. 5 ×4 = 108 cm
3
Total number of bars of soap that can be accommodated in that box =
Volume of the box
Volume of each soap
=
466560
108
= 4320
 bars
Q u e s t i o n : 7
The size of a matchbox is 4 cm × 2.5 cm × 1.5 cm. What is the volume of a packet containing 144 matchboxes? How many such packets can be placed in
a carton of size 1.5 m × 84 cm × 60 cm?
S o l u t i o n :
Volume occupied by a single matchbox = 4 ×2. 5 ×1. 5 = 15 cm
3
Volume of a packet containing 144 matchboxes = 15 ×144 = 2160 cm
3
Volume of the carton = 150 ×84 ×60 = 756000 cm
3
( )
( )
( )
( )
( )
( )
( )
( )
Total number of packets is a carton =
Volume of the carton
Volume of a packet 
= 
75600
2160
= 350
 packets
Q u e s t i o n : 8
How many planks of size 2 m × 25 cm × 8 cm can be prepared from a wooden block 5 m long, 70 cm broad and 32 cm thick, assuming that there is no
wastage?
S o l u t i o n :
Total volume of the block = 500 ×70 ×32 = 1120000 cm
3
 
Total volume of each plank = 200 ×25 ×8 = 40000 cm
3
= 200 ×25 ×8 = 40000 cm
3
? Total number of planks that can be made =
Total volume of the block
Volume of each plank
 = 
1120000
40000
= 28
 planks
Q u e s t i o n : 9
How many bricks, each of size 25 cm × 13.5 cm × 6 cm, will be required to build a wall 8 m long, 5.4 m high and 33 cm thick?
S o l u t i o n :
Volume of the brick = 25 ×13. 5 ×6 = 2025 cm
3
Volume of the wall = 800 ×540 ×33 = 14256000 cm
3
Total number of bricks =
Volume of the wall
Volume of each brick
=
14256000
2025
= 7040
 bricks  
Q u e s t i o n : 1 0
A wall 15 m long, 30 cm wide and 4 m high is made of bricks, each measuring 22 cm × 12.5 cm × 7.5 cm. If 
1
12
of the total volume of the wall consists of mortar, how many bricks are there in the wall?
S o l u t i o n :
Volume of the wall = 1500 ×30 ×400 = 18000000 cm
3
Total quantity of mortar =
1
12
×18000000 = 1500000 cm
3
? Volume of the bricks = 18000000 -1500000 = 16500000 cm
3
Volume of a single brick = 22 ×12. 5 ×7. 5 = 2062. 5 cm
3
? Total number of bricks =
Total volume of the bricks
Volume of a single brick
=
16500000
2062.5
= 8000
 bricks
Q u e s t i o n : 1 1
Find the capacity of a rectangular cistern in litres whose dimensions are 11.2 m × 6 m × 5.8 m. Find the area of the iron sheet required to make the cistern.
S o l u t i o n :
Volume of the cistern = 11. 2 ×6 ×5. 8 = 389. 76 m
3
= 389. 76 ×1000 = 389760
 litres
Area of the iron sheet required to make this cistern = Total surface area of the cistern
= 2 11. 2 ×6 +11. 2 ×5. 8 +6 ×5. 8 = 2 67. 2 +64. 96 +34. 8 = 333. 92 cm
2
Q u e s t i o n : 1 2
The volume of a block of gold is 0.5 m
3
. If it is hammered into a sheet to cover an area of 1 hectare, find the thickness of the sheet.
S o l u t i o n :
Volume of the block = 0. 5 m
3
We know:
 1 hectare = 10000 m
2
Thickness =
Volume
Area
=
0.5
10000
= 0. 00005 m = 0. 005 cm = 0. 05 mm
Q u e s t i o n : 1 3
( )
( ) ( )
The rainfall recorded on a certain day was 5 cm. Find the volume of water that fell on a 2-hectare field.
S o l u t i o n :
Rainfall recorded = 5 cm = 0.05 m
Area of the field = 2 hectare =  2 ×10000 m
2 
 = 20000 m
2
Total rain over the field = Area of the field × Height of the field = 0. 05 × 20000 = 1000 m
3
Q u e s t i o n : 1 4
A river 2 m deep and 45 m wide is flowing at the rate of 3 km/h. Find the quantity of water that runs into the sea per minute.
S o l u t i o n :
Area of the cross-section of river = 45 ×2 = 90 m
2
Rate of flow = 3
 km
hr
=
3×1000
60
= 50 
m
min
Volume of water flowing through the cross-section in one minute = 90 ×50 = 4500 m
3
 per minute
Q u e s t i o n : 1 5
A pit 5 m long and 3.5 m wide is dug to a certain depth. If the volume of earth taken out of it is 14 m
3
, what is the depth of the pit?
S o l u t i o n :
Let the depth of the pit be d m.
Volume = Length × width × depth = 5 m × 3. 5 m × d m
But,
Given volume = 14 m
3
? Depth = d =
volume
length × width
=
14
5×3.5
= 0. 8 m
= 80 cm
Q u e s t i o n : 1 6
A rectangular water tank is 90 cm wide and 40 cm deep. If it can contain 576 litres of water, what is its length?
S o l u t i o n :
Capacity of the water tank = 576 litres = 0. 576 m
3
Width = 90 cm = 0.9 m
Depth = 40 cm = 0.4 m
Length = =
capacity
width×depth
=
0.576
0.9×0.4
= 1. 600 m
Q u e s t i o n : 1 7
A beam of wood is 5 m long and 36 cm thick. It is made of 1.35 m
3
 of wood. What is the width of the beam?
S o l u t i o n :
Volume of the beam = 1. 35 m
3
Length = 5 m
Thickness = 36 cm = 0.36 m
Width = =
volume
thickness×length
=
1.35
5×0.36
= 0. 75 m = 75 cm
Q u e s t i o n : 1 8
The volume of a room is 378 m
3
 and the area of its floor is 84 m
2
. Find the height of the room.
S o l u t i o n :
Volume = height × area
Given:
 Volume  = 378 m
3
Area = 84 m
2
? Height =
volume
area
=
378
84
= 4. 5 m
Q u e s t i o n : 1 9
A swimming pool is 260 m long and 140 m wide. If 54600 cubic metres of water is pumped into it, find the height of the water level in it.
S o l u t i o n :
Length of the pool = 260 m
Width of the pool = 140 m
Volume of water in the pool = 54600 cubic metres
? Height of water =
volume
length×width
=
54600
260×140
= 1. 5
 metres
Q u e s t i o n : 2 0
Find the volume of wood used to make a closed box of outer dimensions 60 cm × 45 cm × 32 cm, the thickness of wood being 2.5 cm all around.
S o l u t i o n :
External length = 60 cm
External width = 45 cm
External height = 32 cm
External volume of the box = 60 ×45 ×32 = 86400 cm
3
Thickness of wood = 2.5 cm
?  Internal length = 60 -(2. 5 ×2) = 55
 cm
Internal width = 45 -(2. 5 ×2) = 40
 cm
Internal height = 32 -(2. 5 ×2) = 27
 cm
Internal volume of the box = 55 × 40 × 27 = 59400 cm
3
Volume of wood = External volume - Internal volume = 86400 - 59400 = 27000 cm
3
Q u e s t i o n : 2 1
Find the volume of iron required to make an open box whose external dimensions are 36 cm × 25 cm × 16.5 cm, the box being 1.5 cm thick throughout. If 1
cm
3
 of iron weighs 8.5 grams, find the weight of the empty box in kilograms.
S o l u t i o n :
External length = 36 cm
External width = 25 cm
External height = 16.5 cm
External volume of the box = 36 × 25 × 16. 5 = 14850 cm
3
Thickness of iron = 1.5 cm
? Internal length = 36 -(1. 5 ×2) = 33
 cm
Internal width = 25 -(1. 5 ×2) = 22
 cm
Internal height = 16. 5 - 1. 5 = 15
 cm  astheboxisopen
Internal volume of the box = 33 × 22 × 15 = 10890 cm
3
Volume of iron = External volume - Internal volume = 14850 - 10890 = 3960 cm
3
Given: 
1 cm
3
 of iron = 8. 5 grams
Total weight of the box = 3960 × 8. 5 = 33660 grams = 33. 66 kilograms
Q u e s t i o n : 2 2
A box with a lid is made of wood which is 3 cm thick. Its external length, breadth and height are 56 cm, 39 cm and 30 cm respectively. Find the capacity of
the box. Also find the volume of wood used to make the box.
S o l u t i o n :
External length = 56 cm
External width = 39 cm
External height = 30 cm
External volume of the box = 56 × 39 × 30 = 65520 cm
3
Thickness of wood = 3 cm
? Internal length = 56 -(3 ×2) = 50
 cm