Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube) - EXERCISE 21.2
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Page 1
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
EXERCISE 21.2 PAGE NO: 21.15
1. Find the volume in cubic metres (cu. m) of each of the cuboids whose dimensions
are:
(i) length = 12 m, breadth = 10 m, height = 4.5 m
(ii) length = 4 m, breadth = 2.5m, height = 50 cm
(iii) length = 10m, breadth = 25 dm, height = 25 cm.
Solution:
(i) Given details are,
Length of a cuboid = 12 m
Breadth of a cuboid = 10m
Height of a cuboid = 4.5 m
By using the formula
Volume of cuboid = l × b × h
= 12 × 10 × 4.5
= 540 m
3
(ii) Given details are,
Length of a cuboid = 4 m
Breadth of a cuboid = 2.5 m
Height of a cuboid = 50 cm = 0.50m
By using the formula
Volume of a cuboid = l × b × h
= 4 × 2.5 × 0.50
= 5 m
3
(iii) Given details are,
Length of a cuboid = 10m
Breadth of a cuboid = 25 dm = 2.5 m
Height of a cuboid = 25 cm = 0.25 m
By using the formula
Volume of a cuboid = l × b × h
= 10 × 2.5 × 0.25
= 6.25 m
3
2. Find the volume in cubic decimetre of each of the cubes whose side is
(i) 1.5 m
(ii) 75cm
(iii) 2 dm 5 cm
Page 2
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
EXERCISE 21.2 PAGE NO: 21.15
1. Find the volume in cubic metres (cu. m) of each of the cuboids whose dimensions
are:
(i) length = 12 m, breadth = 10 m, height = 4.5 m
(ii) length = 4 m, breadth = 2.5m, height = 50 cm
(iii) length = 10m, breadth = 25 dm, height = 25 cm.
Solution:
(i) Given details are,
Length of a cuboid = 12 m
Breadth of a cuboid = 10m
Height of a cuboid = 4.5 m
By using the formula
Volume of cuboid = l × b × h
= 12 × 10 × 4.5
= 540 m
3
(ii) Given details are,
Length of a cuboid = 4 m
Breadth of a cuboid = 2.5 m
Height of a cuboid = 50 cm = 0.50m
By using the formula
Volume of a cuboid = l × b × h
= 4 × 2.5 × 0.50
= 5 m
3
(iii) Given details are,
Length of a cuboid = 10m
Breadth of a cuboid = 25 dm = 2.5 m
Height of a cuboid = 25 cm = 0.25 m
By using the formula
Volume of a cuboid = l × b × h
= 10 × 2.5 × 0.25
= 6.25 m
3
2. Find the volume in cubic decimetre of each of the cubes whose side is
(i) 1.5 m
(ii) 75cm
(iii) 2 dm 5 cm
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
Solution:
(i) Given details are,
Side of cube = 1.5m = 15 dm
So, Volume of cube = 15
3
= 3375 dm
3
(ii) Given details are,
Side of cube = 75cm = 7.5 dm
So, Volume of cube = 7.5
3
= 421.875 dm
3
(iii) Given details are,
Side of cube = 2dm 5cm = 2.5 dm
So, Volume of cube = 2.5
3
= 15.625 dm
3
3. How much clay is dug out in digging a well measuring 3 m by 2 m by 5 m?
Solution:
Given details are,
Dimensions of well = 3m × 2m × 5m
So,
Volume of clay dug out from well is = l × b × h
= 3 × 2 × 5
= 30 m
3
4. What will be the height of a cuboid of volume 168 m
3
, if the area of its base is 28
m
2
?
Solution:
Given details are,
Volume of a cuboid = 168 m
3
Area of base = l × b = 28m
2
Let height of cuboid be ‘h’ m
We know that,
Volume = l × b × h
h = volume/ l × b
= 168/28
= 6m
? Height of cuboid is 6 m
5. A tank is 8 m long, 6 m broad and 2 m high. How much water can it contain?
Solution:
Given details are,
Page 3
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
EXERCISE 21.2 PAGE NO: 21.15
1. Find the volume in cubic metres (cu. m) of each of the cuboids whose dimensions
are:
(i) length = 12 m, breadth = 10 m, height = 4.5 m
(ii) length = 4 m, breadth = 2.5m, height = 50 cm
(iii) length = 10m, breadth = 25 dm, height = 25 cm.
Solution:
(i) Given details are,
Length of a cuboid = 12 m
Breadth of a cuboid = 10m
Height of a cuboid = 4.5 m
By using the formula
Volume of cuboid = l × b × h
= 12 × 10 × 4.5
= 540 m
3
(ii) Given details are,
Length of a cuboid = 4 m
Breadth of a cuboid = 2.5 m
Height of a cuboid = 50 cm = 0.50m
By using the formula
Volume of a cuboid = l × b × h
= 4 × 2.5 × 0.50
= 5 m
3
(iii) Given details are,
Length of a cuboid = 10m
Breadth of a cuboid = 25 dm = 2.5 m
Height of a cuboid = 25 cm = 0.25 m
By using the formula
Volume of a cuboid = l × b × h
= 10 × 2.5 × 0.25
= 6.25 m
3
2. Find the volume in cubic decimetre of each of the cubes whose side is
(i) 1.5 m
(ii) 75cm
(iii) 2 dm 5 cm
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
Solution:
(i) Given details are,
Side of cube = 1.5m = 15 dm
So, Volume of cube = 15
3
= 3375 dm
3
(ii) Given details are,
Side of cube = 75cm = 7.5 dm
So, Volume of cube = 7.5
3
= 421.875 dm
3
(iii) Given details are,
Side of cube = 2dm 5cm = 2.5 dm
So, Volume of cube = 2.5
3
= 15.625 dm
3
3. How much clay is dug out in digging a well measuring 3 m by 2 m by 5 m?
Solution:
Given details are,
Dimensions of well = 3m × 2m × 5m
So,
Volume of clay dug out from well is = l × b × h
= 3 × 2 × 5
= 30 m
3
4. What will be the height of a cuboid of volume 168 m
3
, if the area of its base is 28
m
2
?
Solution:
Given details are,
Volume of a cuboid = 168 m
3
Area of base = l × b = 28m
2
Let height of cuboid be ‘h’ m
We know that,
Volume = l × b × h
h = volume/ l × b
= 168/28
= 6m
? Height of cuboid is 6 m
5. A tank is 8 m long, 6 m broad and 2 m high. How much water can it contain?
Solution:
Given details are,
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
Dimensions of a tank = 8m × 6m × 2m
We know that,
Volume of tank = l × b × h
= 8 × 6 × 2
= 96 m
3
= 96000 litres
? The tank can contain 96000 litres of water.
6. The capacity of a certain cuboidal tank is 50000 litres of water. Find the breadth
of the tank, if its height and length are 10 m and 2.5 m respectively.
Solution:
Given details are,
Capacity (volume) of cuboidal tank is = 50000 litre = 50 m
3
Height of tank = 10 m
Length of tank = 2.5 m
Let breadth of tank be ‘b’ m
We know that,
Volume = l × b × h
b = volume / (l × h)
= 50/(10×2.5)
= 2m
? Breadth of tank is 2m
7. A rectangular diesel tanker is 2m long, 2m wide and 40cm deep. How many litres
of diesel can it hold?
Solution:
Given details are,
Length of a tanker = 2m
Breadth of a tanker = 2m
Height of a tanker = 40cm = 0.4m
So, Dimensions of rectangular diesel tank = 2m × 2m × 0.4m
Volume of tank (amount of diesel it can hold) = l × b × h
= 2 × 2 × 0.4
= 1.6m
3
= 1600 litres
? A rectangular diesel tanker can hold 1600 litres of diesel.
8. The length, breadth and height of a room are 5 m, 4.5 m and 3 m respectively.
Find the volume of the air it contains.
Page 4
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
EXERCISE 21.2 PAGE NO: 21.15
1. Find the volume in cubic metres (cu. m) of each of the cuboids whose dimensions
are:
(i) length = 12 m, breadth = 10 m, height = 4.5 m
(ii) length = 4 m, breadth = 2.5m, height = 50 cm
(iii) length = 10m, breadth = 25 dm, height = 25 cm.
Solution:
(i) Given details are,
Length of a cuboid = 12 m
Breadth of a cuboid = 10m
Height of a cuboid = 4.5 m
By using the formula
Volume of cuboid = l × b × h
= 12 × 10 × 4.5
= 540 m
3
(ii) Given details are,
Length of a cuboid = 4 m
Breadth of a cuboid = 2.5 m
Height of a cuboid = 50 cm = 0.50m
By using the formula
Volume of a cuboid = l × b × h
= 4 × 2.5 × 0.50
= 5 m
3
(iii) Given details are,
Length of a cuboid = 10m
Breadth of a cuboid = 25 dm = 2.5 m
Height of a cuboid = 25 cm = 0.25 m
By using the formula
Volume of a cuboid = l × b × h
= 10 × 2.5 × 0.25
= 6.25 m
3
2. Find the volume in cubic decimetre of each of the cubes whose side is
(i) 1.5 m
(ii) 75cm
(iii) 2 dm 5 cm
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
Solution:
(i) Given details are,
Side of cube = 1.5m = 15 dm
So, Volume of cube = 15
3
= 3375 dm
3
(ii) Given details are,
Side of cube = 75cm = 7.5 dm
So, Volume of cube = 7.5
3
= 421.875 dm
3
(iii) Given details are,
Side of cube = 2dm 5cm = 2.5 dm
So, Volume of cube = 2.5
3
= 15.625 dm
3
3. How much clay is dug out in digging a well measuring 3 m by 2 m by 5 m?
Solution:
Given details are,
Dimensions of well = 3m × 2m × 5m
So,
Volume of clay dug out from well is = l × b × h
= 3 × 2 × 5
= 30 m
3
4. What will be the height of a cuboid of volume 168 m
3
, if the area of its base is 28
m
2
?
Solution:
Given details are,
Volume of a cuboid = 168 m
3
Area of base = l × b = 28m
2
Let height of cuboid be ‘h’ m
We know that,
Volume = l × b × h
h = volume/ l × b
= 168/28
= 6m
? Height of cuboid is 6 m
5. A tank is 8 m long, 6 m broad and 2 m high. How much water can it contain?
Solution:
Given details are,
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
Dimensions of a tank = 8m × 6m × 2m
We know that,
Volume of tank = l × b × h
= 8 × 6 × 2
= 96 m
3
= 96000 litres
? The tank can contain 96000 litres of water.
6. The capacity of a certain cuboidal tank is 50000 litres of water. Find the breadth
of the tank, if its height and length are 10 m and 2.5 m respectively.
Solution:
Given details are,
Capacity (volume) of cuboidal tank is = 50000 litre = 50 m
3
Height of tank = 10 m
Length of tank = 2.5 m
Let breadth of tank be ‘b’ m
We know that,
Volume = l × b × h
b = volume / (l × h)
= 50/(10×2.5)
= 2m
? Breadth of tank is 2m
7. A rectangular diesel tanker is 2m long, 2m wide and 40cm deep. How many litres
of diesel can it hold?
Solution:
Given details are,
Length of a tanker = 2m
Breadth of a tanker = 2m
Height of a tanker = 40cm = 0.4m
So, Dimensions of rectangular diesel tank = 2m × 2m × 0.4m
Volume of tank (amount of diesel it can hold) = l × b × h
= 2 × 2 × 0.4
= 1.6m
3
= 1600 litres
? A rectangular diesel tanker can hold 1600 litres of diesel.
8. The length, breadth and height of a room are 5 m, 4.5 m and 3 m respectively.
Find the volume of the air it contains.
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
Solution:
Given details are,
Length of a room = 5m
Breadth of a room = 4.5m
Height of a room = 3m
So, Dimensions of a room are = 5m × 4.5m × 3m
Volume of air = l × b × h
= 5 × 4.5 × 3
= 67.5m
3
? The room contains 67.5m
3
volume of the air.
9. A water tank is 3 m long, 2 m broad and 1 m deep. How many litres of water can
it hold?
Solution:
Given details are,
Length of water tank = 3m
Breadth of water tank = 2m
Height of water tank = 1m
So, Dimensions of water tank is = 3m × 2m × 1m
Volume the water tank can hold = l × b × h
= 3 × 2 × 1
= 6m
3
= 6000 litres
? The water tank can hold 6000 litres of water.
10. How many planks each of which is 3 m long, 15 cm broad and 5 cm thick can be
prepared from a wooden block 6 m long, 75 cm broad and 45 cm thick?
Solution:
Given details are,
Dimensions of one plank = 3m × 15cm × 5cm = 300cm × 15cm × 5cm
Dimensions of wooden block = 6m × 75cm × 45cm = 600cm × 75cm × 45cm
We know that,
Number of planks that can be prepared = volume of wooden block / volume of one plank
= (600 × 75 × 45) / (300 × 15 × 5)
= 90 planks
? 90 planks are required to prepare the block.
11. How many bricks each of size 25 cm × 10 cm × 8 cm will be required to build a
wall 5 m long, 3 m high and 16 cm thick, assuming that the volume of sand and
Page 5
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
EXERCISE 21.2 PAGE NO: 21.15
1. Find the volume in cubic metres (cu. m) of each of the cuboids whose dimensions
are:
(i) length = 12 m, breadth = 10 m, height = 4.5 m
(ii) length = 4 m, breadth = 2.5m, height = 50 cm
(iii) length = 10m, breadth = 25 dm, height = 25 cm.
Solution:
(i) Given details are,
Length of a cuboid = 12 m
Breadth of a cuboid = 10m
Height of a cuboid = 4.5 m
By using the formula
Volume of cuboid = l × b × h
= 12 × 10 × 4.5
= 540 m
3
(ii) Given details are,
Length of a cuboid = 4 m
Breadth of a cuboid = 2.5 m
Height of a cuboid = 50 cm = 0.50m
By using the formula
Volume of a cuboid = l × b × h
= 4 × 2.5 × 0.50
= 5 m
3
(iii) Given details are,
Length of a cuboid = 10m
Breadth of a cuboid = 25 dm = 2.5 m
Height of a cuboid = 25 cm = 0.25 m
By using the formula
Volume of a cuboid = l × b × h
= 10 × 2.5 × 0.25
= 6.25 m
3
2. Find the volume in cubic decimetre of each of the cubes whose side is
(i) 1.5 m
(ii) 75cm
(iii) 2 dm 5 cm
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
Solution:
(i) Given details are,
Side of cube = 1.5m = 15 dm
So, Volume of cube = 15
3
= 3375 dm
3
(ii) Given details are,
Side of cube = 75cm = 7.5 dm
So, Volume of cube = 7.5
3
= 421.875 dm
3
(iii) Given details are,
Side of cube = 2dm 5cm = 2.5 dm
So, Volume of cube = 2.5
3
= 15.625 dm
3
3. How much clay is dug out in digging a well measuring 3 m by 2 m by 5 m?
Solution:
Given details are,
Dimensions of well = 3m × 2m × 5m
So,
Volume of clay dug out from well is = l × b × h
= 3 × 2 × 5
= 30 m
3
4. What will be the height of a cuboid of volume 168 m
3
, if the area of its base is 28
m
2
?
Solution:
Given details are,
Volume of a cuboid = 168 m
3
Area of base = l × b = 28m
2
Let height of cuboid be ‘h’ m
We know that,
Volume = l × b × h
h = volume/ l × b
= 168/28
= 6m
? Height of cuboid is 6 m
5. A tank is 8 m long, 6 m broad and 2 m high. How much water can it contain?
Solution:
Given details are,
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
Dimensions of a tank = 8m × 6m × 2m
We know that,
Volume of tank = l × b × h
= 8 × 6 × 2
= 96 m
3
= 96000 litres
? The tank can contain 96000 litres of water.
6. The capacity of a certain cuboidal tank is 50000 litres of water. Find the breadth
of the tank, if its height and length are 10 m and 2.5 m respectively.
Solution:
Given details are,
Capacity (volume) of cuboidal tank is = 50000 litre = 50 m
3
Height of tank = 10 m
Length of tank = 2.5 m
Let breadth of tank be ‘b’ m
We know that,
Volume = l × b × h
b = volume / (l × h)
= 50/(10×2.5)
= 2m
? Breadth of tank is 2m
7. A rectangular diesel tanker is 2m long, 2m wide and 40cm deep. How many litres
of diesel can it hold?
Solution:
Given details are,
Length of a tanker = 2m
Breadth of a tanker = 2m
Height of a tanker = 40cm = 0.4m
So, Dimensions of rectangular diesel tank = 2m × 2m × 0.4m
Volume of tank (amount of diesel it can hold) = l × b × h
= 2 × 2 × 0.4
= 1.6m
3
= 1600 litres
? A rectangular diesel tanker can hold 1600 litres of diesel.
8. The length, breadth and height of a room are 5 m, 4.5 m and 3 m respectively.
Find the volume of the air it contains.
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
Solution:
Given details are,
Length of a room = 5m
Breadth of a room = 4.5m
Height of a room = 3m
So, Dimensions of a room are = 5m × 4.5m × 3m
Volume of air = l × b × h
= 5 × 4.5 × 3
= 67.5m
3
? The room contains 67.5m
3
volume of the air.
9. A water tank is 3 m long, 2 m broad and 1 m deep. How many litres of water can
it hold?
Solution:
Given details are,
Length of water tank = 3m
Breadth of water tank = 2m
Height of water tank = 1m
So, Dimensions of water tank is = 3m × 2m × 1m
Volume the water tank can hold = l × b × h
= 3 × 2 × 1
= 6m
3
= 6000 litres
? The water tank can hold 6000 litres of water.
10. How many planks each of which is 3 m long, 15 cm broad and 5 cm thick can be
prepared from a wooden block 6 m long, 75 cm broad and 45 cm thick?
Solution:
Given details are,
Dimensions of one plank = 3m × 15cm × 5cm = 300cm × 15cm × 5cm
Dimensions of wooden block = 6m × 75cm × 45cm = 600cm × 75cm × 45cm
We know that,
Number of planks that can be prepared = volume of wooden block / volume of one plank
= (600 × 75 × 45) / (300 × 15 × 5)
= 90 planks
? 90 planks are required to prepare the block.
11. How many bricks each of size 25 cm × 10 cm × 8 cm will be required to build a
wall 5 m long, 3 m high and 16 cm thick, assuming that the volume of sand and
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
cement used in the construction is negligible?
Solution:
Given details are,
Size of one brick = 25cm × 10cm × 8cm
Dimensions of wall = 5m × 3m × 16cm = 500 cm × 300 cm × 16cm
We know that,
Number of bricks required to build a wall = volume of wall / volume of one brick
= (500×300×16) / (25×10×8)
= 1200 bricks
? 1200 bricks are required to build the wall.
12. A village, having a population of 4000, required 150 litres water per head per
day. It has a tank which is 20 m long, 15 m broad and 6 m high. For how many days
will the water of this tank last?
Solution:
Given details are,
Population of village = 4000
Dimensions of water tank = 20m × 15m × 6m
Water required per head per day = 150 litres
Total requirement of water per day = 150 × 4000 = 600000 litres
Volume of water tank = l × b × h
= 20 × 15 × 6
= 1800m
3
= 1800000 litres
We know that,
Number of days water last in the tank = volume of tank / total requirement
= 1800000/600000
= 3 days
? Water in the tank last for 3 days.
13. A rectangular field is 70 m long and 60 m broad. A well of dimensions 14 m × 8
m × 6 m is dug outside the field and the earth dug-out from this well is spread
evenly on the field. How much will the earth level rise?
Solution:
Given details are,
Dimensions of rectangular field = 70m × 60m
Dimensions of well = 14m × 8m × 6m
Amount of earth dug out from well (volume) = l × b × h
= 14 × 8 × 6 = 672m
3
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Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube) - EXERCISE 21.2 Notes
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Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube) - EXERCISE 21.2 Class 8 Questions
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