We all are familiar with the definition of volume i.e. it is the amount of space occupied by an object. In this article, you will find various questions asked on the volume of cube and cuboid. Worksheet on Volume of Cube and Cuboid has got a plethora of questions ranging from easy to hard levels. You can use them to quickly understand the concept as well as learn how to solve word problems on the Volume of Cubes and Cuboids in no time. Practice the Problems on Cube and Cuboid Volume and attempt the exam with utmost confidence and clear with flying colors.
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Volume of a Cube and Cuboid Questions and Answers
Example 1.
Find the volume of a cube whose each edge is
(i) 4 cm
(ii) 6 cm
(iii) 8 cm
Solution:
We know the volume of the cube v=s3 where s is the edge length of the cube.
(i) Given edge s=4 cm
volume=4 3
=64
Hence, the volume of the cube is 64
(ii) Given,edge s=6 cm
volume=6 3
=216
Hence, the volume of the cube is 216
(iii) Given, edge s=8 cm
volume=83
=512
Hence, the volume of the cube is 512.
Example 2.
Find the volume of the cuboid whose dimensions are
(i) length=8 inches, breadth=5 inches, height=3 inches
(ii) length=12 inches,breadth=15inches , height=13 inches
(iii) length=23 inches,breadth=12 inches, height=18 inches
Solution:
(i) Given,
The length of the cuboid=8 inches
The breadth of the cuboid=5 inches
The height of the cuboid=3 inches
we know that volume of the cuboid v=lbh
volume v=(8.5.3)in3=120 in3
Hence, the volume of the cuboid is 120 in3.
(ii) Given,
The length of the cuboid=12 inches
The breadth of the cuboid=15 inches
The height of the cuboid=13 inches
we know that volume of the cuboid v=lbh
volume v=(12.15.13)in3=2340 in3
Hence, the volume of the cuboid is 2340 in3.
(iii) Given,
The length of the cuboid=23 inches
The breadth of the cuboid=12 inches
The height of the cuboid=18 inches
we know that volume of the cuboid v=lbh
volume v=(23.12.18)in3=4968 in3
Hence, the volume of the cuboid is 4968 in3.
Example 3.
A cube with an edge of 6 cm and a cuboid measuring 5 cm × 3 cm × 7 cm are kept on a table. Which shape has more volume?
Solution:
Given,
Edge of the cube=6 cm
The Length of the cuboid=5 cm
The breadth of the cuboid=3 cm
The height of the cuboid=7 cm
We know that volume of the cube= edge3
=63
=216 cm3
As we know the volume of the cuboid=lbh
=5 cm.3 cm.7 cm
=105 cm3
Hence, the volume of the cube has more volume.
Example 4.
Harish’s shelf is 30 cm long, 40 cm wide,50 cm in height. Find the volume of the shelf?
Solution:
Given,
Length of the shelf=30 cm
width of the shelf=40 cm
height of the shelf=50 cm
The volume of the shelf=l.b.h
=30 cm.40 cm.50 cm
=60,000 cm3
Hence, the volume of Harish’s shelf is 60,000 cm3.
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Example 5.
Water pond is 40 meters long,15 meters in width, and 10 meters in height. Find the capacity of the water pond in cubic meters?
Solution:
Given,
Length of the water pond=40 meters
width of the water pond=15 meters
height of the water pond=10 meters
The capacity of the water pond=l.b.h
=40.15.10 m3
=6,000 m3
1000 lit=1 m3
=6,000(1000)
=60,00,000 liters
Hence, the capacity of the water pond is 60,00,000 liters.
Example 6.
The volume of the container is 3000 m3. The length and breadth of the container are 20 m and 10 m respectively. Find the height of the container?
Solution:
Given,
The volume of the container=3000 m3
The length of the container=20 m
The breadth of the container=10 m
The height of the container=?
We know that volumr=lbh
Let the height of the container be x.
20.10.x=3000
200x=3000
x=3000/200
=15 m
Therefore, the height of the container is 15 m.
Example 7.
A cubical water tank can hold 512000 liters of water. Find the length of its side in meters?
Solution:
The volume of the water tank=512000 liters
1 m3=1000 liters
The volume of the tank in m3= 512000/1000
a3=512
a=8
Hence, the length of the side of the water tank is 8 meters.
Example 8.
A metallic cube with a side of 10 cm is melted and formed into a cuboid. If the length and height of the cuboid are 15 cm and 10 cm respectively then find the breadth of the cuboid?
Solution:
Given,
metallic cube side=10 cm
length of the cuboid=5 cm
height of the cuboid=10 cm
The volume of cube=volume of cuboid
a3=103
Volume of cube=1000
length.breadth.height=1000
5 .breadth.10 =1000
breadth=1000/50=20 m
Hence, breadth of the cuboid is 20 meters.
Example 9.
If the length of the side of the cube is 5 cm. Find its lateral surface area?
Solution:
Given,
side of the cube=5 cm
Volume of cube = side3 = 53
=125
The volume of the cube is 125 cubic cm.
Example 10.
The length, breadth, and height of a wooden box are in the ratio 6: 5 : 3. If its volume is 11250 cm3, then find its dimensions?
Solution:
Given,
The length, breadth, height of the wooden box are in the ratio 6: 5 : 3
Volume=11250 cm3
Let 6x,5x,3x be the length, breadth, and height of a wooden box.
6x.5x.3x=11250
90x3=11250
x3=11250/90=125
x=5 cm
length=6x=6(5)=30 cm
breadth=5x=5(5)=25 cm
height=3x=3(3)=9 cm
Hence, the length,breadth,and height of the wooden box are 30cm,25cm,9cm.
Example 11.
The volume of a cuboid is twice the volume of a cube. If the dimensions of the cuboid are 2 cm, 25 cm, and5 cm. the total surface area of the cube?
Solution:
Given,
The dimensions of the cuboid are 2cm,25 cm, and 5 cm.
The volume of the cuboid=lbh
=2.25.5
=250 cm3
Also given, The volume of a cuboid is twice the volume of a cube.
The volume of cube=volume of cuboid/2
=250/2=125 cm3
The volume of the cube=a3
a3=125
a=5
The total surface area of the cube=6a2
=6(5)2
=150 cm2
Hence, the total surface area of the cube is 150 cm2.
Example 12.
If a cube and cuboid have the same area and the volume of a cube is 125 cm3 while that of a cuboid is 50 cm3. Find the height of the cuboid?
       
Solution:
Let each edge of a cube =a cm and length bredth and heught of a cuboid are l ,b and h cm. Acordingly Volume of cube= a3=125 cm3
a=5cm…………………(1)
Volume of cuboid =l×b×h cm3
l.b.h =50 cm3………………(2)
Area of base of cube =a^2 cm2
Area of base of cuboid =l×b cm2.
l.b=a2 , put a=5 cm from eq.(1).
l.b=(5 cm)2
l.b =25 cm 2…………………..(3)
Divide eq.(2) by eq (3)
l.b.h/l.b =50 cm3/25 cm2
h = 2 cm
Hence, the height of the cuboid is 2 cm.