ML Aggarwal: Mensuration - 3

 Page 1


 
1. The volume of a cube is 343 cm
3
, find the length of an edge of 
cube. 
Solution: 
Given, 
Volume of a cube = 343 cm
3
 
 
Let’s consider ‘a’ to be the edge of cube, then 
 
V = a
3
 = 343 = (7)
3
  
 
? a = 7 cm 
  
2. Fill in the following blanks: 
 
Volume of cuboid Length Breadth Height 
(i) 90 cm
3
 – 5 cm 3 cm 
(ii) – 15 cm 8 cm 7 cm 
(iii) 62.5 m
3
 10 cm 5 cm – 
Solution: 
Volume of cuboid = length × Breadth × Height 
(i) 90 cm
3
 = length × 5 cm × 3 cm 
Length = 

× 
=

	
= 6 cm 
(ii) Volume = 15 cm × 8 cm × 7 cm 
= 840 cm
3
 
(iii) 62.5 m
3
 = 10 m × 5 m × height 
Height = 
.
	×
 = 1.25 m 
Page 2


 
1. The volume of a cube is 343 cm
3
, find the length of an edge of 
cube. 
Solution: 
Given, 
Volume of a cube = 343 cm
3
 
 
Let’s consider ‘a’ to be the edge of cube, then 
 
V = a
3
 = 343 = (7)
3
  
 
? a = 7 cm 
  
2. Fill in the following blanks: 
 
Volume of cuboid Length Breadth Height 
(i) 90 cm
3
 – 5 cm 3 cm 
(ii) – 15 cm 8 cm 7 cm 
(iii) 62.5 m
3
 10 cm 5 cm – 
Solution: 
Volume of cuboid = length × Breadth × Height 
(i) 90 cm
3
 = length × 5 cm × 3 cm 
Length = 

× 
=

	
= 6 cm 
(ii) Volume = 15 cm × 8 cm × 7 cm 
= 840 cm
3
 
(iii) 62.5 m
3
 = 10 m × 5 m × height 
Height = 
.
	×
 = 1.25 m 
 
Volume of cuboid Length Breadth Height 
(i) 90 cm
3
 6 cm 5 cm 3 cm 
(ii) 840 cm
3
 15 cm 8 cm 7 cm 
(iii) 62.5 m
3
 10 cm 5 cm 1.25 m 
 
3. Find the height of a cuboid whose volume is 312 cm
3
 and base area 
is 26 cm
2
. 
Solution: 
Given, 
Volume of a cuboid = 312 cm
3
 
 
Base area = l × b = 26 cm
2
 
 
? Height= Volume/Base area = 
	

 = 12cm 
 
4. A godown is in the form of a cuboid of measures 55 m × 45 m × 30 
m. How many cuboidal boxes can be stored in it if the volume of one 
box is 1.25 m
3
? 
Solution: 
Given, 
 
Length of a godown (l) = 55 m 
 
Breadth (b) = 45 m 
 
Height (h) = 30 m 
 
So, 
Volume = l × b × h 
Page 3


 
1. The volume of a cube is 343 cm
3
, find the length of an edge of 
cube. 
Solution: 
Given, 
Volume of a cube = 343 cm
3
 
 
Let’s consider ‘a’ to be the edge of cube, then 
 
V = a
3
 = 343 = (7)
3
  
 
? a = 7 cm 
  
2. Fill in the following blanks: 
 
Volume of cuboid Length Breadth Height 
(i) 90 cm
3
 – 5 cm 3 cm 
(ii) – 15 cm 8 cm 7 cm 
(iii) 62.5 m
3
 10 cm 5 cm – 
Solution: 
Volume of cuboid = length × Breadth × Height 
(i) 90 cm
3
 = length × 5 cm × 3 cm 
Length = 

× 
=

	
= 6 cm 
(ii) Volume = 15 cm × 8 cm × 7 cm 
= 840 cm
3
 
(iii) 62.5 m
3
 = 10 m × 5 m × height 
Height = 
.
	×
 = 1.25 m 
 
Volume of cuboid Length Breadth Height 
(i) 90 cm
3
 6 cm 5 cm 3 cm 
(ii) 840 cm
3
 15 cm 8 cm 7 cm 
(iii) 62.5 m
3
 10 cm 5 cm 1.25 m 
 
3. Find the height of a cuboid whose volume is 312 cm
3
 and base area 
is 26 cm
2
. 
Solution: 
Given, 
Volume of a cuboid = 312 cm
3
 
 
Base area = l × b = 26 cm
2
 
 
? Height= Volume/Base area = 
	

 = 12cm 
 
4. A godown is in the form of a cuboid of measures 55 m × 45 m × 30 
m. How many cuboidal boxes can be stored in it if the volume of one 
box is 1.25 m
3
? 
Solution: 
Given, 
 
Length of a godown (l) = 55 m 
 
Breadth (b) = 45 m 
 
Height (h) = 30 m 
 
So, 
Volume = l × b × h 
= (55 × 45 × 30) m
3
 
= 74250 m
3
 
 
Also given, volume of one box = 1.25 m
3
 
 
Thus, 
Number of boxes = 

	.
 = 59400 boxes 
  
5. A rectangular pit 1.4 m long, 90 cm broad and 70 cm deep was dug 
and 1000 bricks of base 21 cm by 10.5 cm were made from the earth 
dug out. Find the height of each brick. 
Solution: 
Here l = 1.4 m = 140 cm, b = 90 cm and h = 70 cm 
Volume of rectangular pit = l × b × h 
= (140 × 90 × 70) cm
3
  
= 882000 cm
3
 
Volume of brick = 21 × 10.5 × h 
Now, 
Number of bricks = 
  
  
 
1000 = 

	 × 	. ×  !
 
      h = 

	 × 	. × 	!
 
         = 4 cm 
Thus, the height of each brick is 4 cm. 
Page 4


 
1. The volume of a cube is 343 cm
3
, find the length of an edge of 
cube. 
Solution: 
Given, 
Volume of a cube = 343 cm
3
 
 
Let’s consider ‘a’ to be the edge of cube, then 
 
V = a
3
 = 343 = (7)
3
  
 
? a = 7 cm 
  
2. Fill in the following blanks: 
 
Volume of cuboid Length Breadth Height 
(i) 90 cm
3
 – 5 cm 3 cm 
(ii) – 15 cm 8 cm 7 cm 
(iii) 62.5 m
3
 10 cm 5 cm – 
Solution: 
Volume of cuboid = length × Breadth × Height 
(i) 90 cm
3
 = length × 5 cm × 3 cm 
Length = 

× 
=

	
= 6 cm 
(ii) Volume = 15 cm × 8 cm × 7 cm 
= 840 cm
3
 
(iii) 62.5 m
3
 = 10 m × 5 m × height 
Height = 
.
	×
 = 1.25 m 
 
Volume of cuboid Length Breadth Height 
(i) 90 cm
3
 6 cm 5 cm 3 cm 
(ii) 840 cm
3
 15 cm 8 cm 7 cm 
(iii) 62.5 m
3
 10 cm 5 cm 1.25 m 
 
3. Find the height of a cuboid whose volume is 312 cm
3
 and base area 
is 26 cm
2
. 
Solution: 
Given, 
Volume of a cuboid = 312 cm
3
 
 
Base area = l × b = 26 cm
2
 
 
? Height= Volume/Base area = 
	

 = 12cm 
 
4. A godown is in the form of a cuboid of measures 55 m × 45 m × 30 
m. How many cuboidal boxes can be stored in it if the volume of one 
box is 1.25 m
3
? 
Solution: 
Given, 
 
Length of a godown (l) = 55 m 
 
Breadth (b) = 45 m 
 
Height (h) = 30 m 
 
So, 
Volume = l × b × h 
= (55 × 45 × 30) m
3
 
= 74250 m
3
 
 
Also given, volume of one box = 1.25 m
3
 
 
Thus, 
Number of boxes = 

	.
 = 59400 boxes 
  
5. A rectangular pit 1.4 m long, 90 cm broad and 70 cm deep was dug 
and 1000 bricks of base 21 cm by 10.5 cm were made from the earth 
dug out. Find the height of each brick. 
Solution: 
Here l = 1.4 m = 140 cm, b = 90 cm and h = 70 cm 
Volume of rectangular pit = l × b × h 
= (140 × 90 × 70) cm
3
  
= 882000 cm
3
 
Volume of brick = 21 × 10.5 × h 
Now, 
Number of bricks = 
  
  
 
1000 = 

	 × 	. ×  !
 
      h = 

	 × 	. × 	!
 
         = 4 cm 
Thus, the height of each brick is 4 cm. 
6. If each edge of a cube is tripled, then find how many times will its 
volume become? 
Solution: 
Let’s consider the edge of a cube to be x 
 
Then, it’s volume = x
3
 
 
Now, if the edge is tripled 
 
Edge = 3x 
 
So, volume = (3x)
3
 = 27x
3
 
 
? Its volume is 27 times the volume of the given cube. 
 
7. A milk tank is in the form of cylinder whose radius is 1.4 m and 
height is 8 m. find the quantity of milk in litres that can be stored in 
the tank. 
Solution: 
Given, 
Radius of the milk cylindrical tank = 1.4 m and height (h) = 8 m 
Hence, 
Volume of milk in the tank = pr
2
h 
= "


# × 1.4 × 1.4 × 8 m
3
 
= 49.28 m
3
 
= 49.28 × 1000 litres 
= 49280 litres 
Therefore, the quantity of the tank is 49280 litres. 
Page 5


 
1. The volume of a cube is 343 cm
3
, find the length of an edge of 
cube. 
Solution: 
Given, 
Volume of a cube = 343 cm
3
 
 
Let’s consider ‘a’ to be the edge of cube, then 
 
V = a
3
 = 343 = (7)
3
  
 
? a = 7 cm 
  
2. Fill in the following blanks: 
 
Volume of cuboid Length Breadth Height 
(i) 90 cm
3
 – 5 cm 3 cm 
(ii) – 15 cm 8 cm 7 cm 
(iii) 62.5 m
3
 10 cm 5 cm – 
Solution: 
Volume of cuboid = length × Breadth × Height 
(i) 90 cm
3
 = length × 5 cm × 3 cm 
Length = 

× 
=

	
= 6 cm 
(ii) Volume = 15 cm × 8 cm × 7 cm 
= 840 cm
3
 
(iii) 62.5 m
3
 = 10 m × 5 m × height 
Height = 
.
	×
 = 1.25 m 
 
Volume of cuboid Length Breadth Height 
(i) 90 cm
3
 6 cm 5 cm 3 cm 
(ii) 840 cm
3
 15 cm 8 cm 7 cm 
(iii) 62.5 m
3
 10 cm 5 cm 1.25 m 
 
3. Find the height of a cuboid whose volume is 312 cm
3
 and base area 
is 26 cm
2
. 
Solution: 
Given, 
Volume of a cuboid = 312 cm
3
 
 
Base area = l × b = 26 cm
2
 
 
? Height= Volume/Base area = 
	

 = 12cm 
 
4. A godown is in the form of a cuboid of measures 55 m × 45 m × 30 
m. How many cuboidal boxes can be stored in it if the volume of one 
box is 1.25 m
3
? 
Solution: 
Given, 
 
Length of a godown (l) = 55 m 
 
Breadth (b) = 45 m 
 
Height (h) = 30 m 
 
So, 
Volume = l × b × h 
= (55 × 45 × 30) m
3
 
= 74250 m
3
 
 
Also given, volume of one box = 1.25 m
3
 
 
Thus, 
Number of boxes = 

	.
 = 59400 boxes 
  
5. A rectangular pit 1.4 m long, 90 cm broad and 70 cm deep was dug 
and 1000 bricks of base 21 cm by 10.5 cm were made from the earth 
dug out. Find the height of each brick. 
Solution: 
Here l = 1.4 m = 140 cm, b = 90 cm and h = 70 cm 
Volume of rectangular pit = l × b × h 
= (140 × 90 × 70) cm
3
  
= 882000 cm
3
 
Volume of brick = 21 × 10.5 × h 
Now, 
Number of bricks = 
  
  
 
1000 = 

	 × 	. ×  !
 
      h = 

	 × 	. × 	!
 
         = 4 cm 
Thus, the height of each brick is 4 cm. 
6. If each edge of a cube is tripled, then find how many times will its 
volume become? 
Solution: 
Let’s consider the edge of a cube to be x 
 
Then, it’s volume = x
3
 
 
Now, if the edge is tripled 
 
Edge = 3x 
 
So, volume = (3x)
3
 = 27x
3
 
 
? Its volume is 27 times the volume of the given cube. 
 
7. A milk tank is in the form of cylinder whose radius is 1.4 m and 
height is 8 m. find the quantity of milk in litres that can be stored in 
the tank. 
Solution: 
Given, 
Radius of the milk cylindrical tank = 1.4 m and height (h) = 8 m 
Hence, 
Volume of milk in the tank = pr
2
h 
= "


# × 1.4 × 1.4 × 8 m
3
 
= 49.28 m
3
 
= 49.28 × 1000 litres 
= 49280 litres 
Therefore, the quantity of the tank is 49280 litres. 
8. A closed box is made of 2 cm thick wood with external dimension 
84 cm × 75 cm × 64 cm. Find the volume of the wood required to make 
the box. 
Solution: 
Given, 
Thickness of the wood used in a closed box = 2 cm 
 
External length of box (L) = 84 cm 
 
Breadth (b) = 75 cm and height (h) = 64 cm 
 
So, internal length (l) = 84 – (2 × 2) 
= 84 – 4 
= 80 cm 
 
Breadth (b) = 75 – (2 × 2) 
= 75 – 4 
= 71 cm 
 
and height (h) = 64 – (2 × 2) 
= 64 – 4 
= 60 cm 
 
Hence, Volume of wood used = 84 × 75 × 64 – 80 × 71 × 60 cm
3
 
 
= 403200 – 340800 cm
3
 
 
= 62400 cm
3