# Worked-out Problems on Volume of a Cuboid | How to Find Cuboid Volume?

Students who want to learn the volume of cuboids and cubes can use the Worked-out Problems on Volume of a Cuboid here. Get to see various examples on the cuboid volume in the coming sections. Try to solve the questions and improve your preparation standards. Check out the Cube and Cuboid Word Problems with solutions in the below sections.

Question 1.

Find the volume of a cuboid of length 18 cm, breadth 25 cm, and height 5 cm?

Solution:

Given that,

Length of cuboid = 18 cm

Breadth of cuboid = 25 cm

Height of cuboid = 5 cm

Cuboid volume = length x breadth x height

Volume = 18 x 25 x 5

= 2250

Therefore, the volume of a cuboid is 2250 cm³.

Question 2.

If the area of the base and height of the cuboid is 212 cm², 8 cm, calculate cuboid volume?

Solution:

Given that,

The base of the base = 212 cm²

Height of a cuboid = 8 cm

Cuboid volume = (Area of the base) x height

Volume = 212 x 8 = 1696 cm³.

Question 3.

Find the volume of the cube whose each side is 16 cm?

Solution:

Given that,

Side length of cube a = 16 cm

The volume of the cube V = a³

V = 16³ = 16 x 16 x 16

V = 4096 cm³

Therefore, the cube volume is 4096 cm³.

Question 4.

If the cuboid volume is 512 cm³, its length and height is 8 cm, 7 cm. Find the cuboid breadth?

Solution:

Given that,

Cuboid Volume = 512 cm³

Cuboid length = 8 cm

Cuboid height = 7 cm

Cuboid breadth = Volume / (length) x (height)

= 512 / (8 x 7)

= 512 / 56 = 9.142 cm

Therefore, the breadth of cuboid is 9.142 cm.

Question 5.

The length, breadth, and depth of a lake are 15 m, 20 m, 9 m respectively. Find the capacity of the lake in liters?

Solution:

Given that,

Length of lake = 15 m

Breadth of lake = 20 m

Depth of lake = 9 m

Capacity of lake = (length) x (breadth) x (depth)

= 15 x 20 x 9 = 2700 m³

1000 liter = 1 m³

Capacity of lake in Litres = 2700 x 1000

= 2700000 litres

Therefore, the capacity of lake is 2700000 litres.

Question 6.

The dimensions of the brick are 25 cm x 8 cm x 10 cm. How many such bricks are required to build a wall of 16 m in length, 20 cm breadth, and 8 m in height?

Solution:

Given that,

Length of brick = 25 cm

Breadth of brick = 8 cm

Height of brick = 10 cm

Length of wall = 16 m

Breadth of wall = 20 m

Height of wall = 8 m

Volume of 1 brick = length x breadth x height

= 25 x 8 x 10 = 2000 cm³

Volume of wall = length x breadth x height

= 16 x 20 x 8

= 2560 = 2560 x 100²

Number of bricks required = (2560 x 100²) / 2000

= 1280 x 10 = 12800

So, the required number of bricks are 12800.

Question 7.

External dimensions of a wooden cuboid are 20 cm × 15 cm × 12 cm. If the thickness of the wood is 2 cm all around, find the volume of the wood contained in the cuboid formed.

Solution:

Given that,

External length of cuboid = 20 cm

External breadth of cuboid = 15 cm

External height of the cuboid = 12 cm

External volume of the cuboid = (length x breadth x height)

= (20 x 15 x 12) = 3600 cm³

Internal length of cuboid = 20 – 4 = 16 cm

Internal breadth of cuboid = 15 – 4 = 11 cm

Internal height of the cuboid = 12 – 4 = 8 cm

Internal volume of a cuboid = (length x breadth x height)

= (16 x 11 x 8) = 1408 cm³

Therefore, volume of wood = External volume of the cuboid – Internal volume of a cuboid

= 3600 – 1408 = 2192 cm³

∴ Volume of the wood contained in the cuboid is 2192 cm³.

Question 8.

The volume of a container is 1440 m³. The length and breadth of the container are 15 m and 8 m respectively. Find its height?

Solution:

Given that,

Length of the container = 15 m

The breadth of the container = 8 m

The volume of the container = 1440 m³

(length x breadth x height) = 1440

15 x 8 x height = 1440

120 x height = 1440

height = 1440/120

height = 12

∴ The height of the container is 12 m.