Mensuration – Volume of Cube, Cuboid, and Cylinder | Class 8 Maths

Mensuration is the branch of mathematics which deals with the study of different geometrical shapes, their areas, and volume. It uses geometric calculations and algebraic equations to compute the measurement of various aspects of objects like Surface Area, Volume, etc. 

Volume is the measurement of the amount of space inside a 3D object that can be filled. It can be the measurement of any solid object like cube, square, cylinder, sphere, pyramid, etc. Volume of an object is usually measured using cubic units. By finding out the volume of an object it also helps us find the amount required to fill an object

The S.I. unit of volume is m³. Other units are ml or L.

Note: 1m³ = 1000 Litre

How to Find Volumes of 3D Objects

Till now you must have understood the meaning of volume, let’s move to find the volume of various 3D geometrical figures like cubes, cuboids, and cylinders.

Finding Volume of a Cuboid

A cuboid is a three-dimensional structure having six rectangular faces. The volume of a cuboid is equal to the product of length, breadth, and height of the cuboid. In rectangular cuboid, all the angles are at right angles and the opposite faces of a cuboid are equal.

Let l is the length, b is the breadth and h is the height of the cuboid.

Let’s consider some example related to the calculation of volume of cuboid.

Example 1: Calculate the volume of the cuboid where length, breadth, and height are 12, 8, and 4 meters respectively.

Solution:

Given, Length=12m

Breadth = 8m

Height = 4m

Applying the Formula,

Volume of cuboid = length × breadth × height

⇒ Volume of cuboid = 12 × 8 × 4 = 384 m³

Thus, volume of the given cuboid is 383 m³.

Example 2: Calculate the breadth of the cuboid whose volume is given as 350-meter cube. And length and height are 7 and 5 meters respectively.

Solution:

Given Volume of cuboid = length × breadth × height

350 = 7 × breadth × 5

⇒ 350/35 = breadth

⇒ 10m = breadth

Thus, breadth of the given cuboid is 10 m.

Volume of a Cube

Firstly the question arises what is cube? So, Cube is a  three-dimensional shape with equal width, height, and length measurements. Basically, a cuboid whose length, width, and height are equal is called a cube.

Since we know the volume of cuboid = length × breadth × height and the cube is a special case of cuboid where all length, breadth, and height are equal. Let’s assume length = breadth = height = a

Let’s consider some example related to the calculation of volume of cube.

Example 1: Find the volume of a cube with sides of length 10 cm.

Solution:

We know, V = (a³)

⇒ V = (10³) cm³

So, Volume of the given cube is 300 centimeter cube

Example 2: Find the length of the sides of the cube whose volume is 343centimeter cube

Solution :

As we know, Volume of cube = side³

343= (side)³

⇒ 7 cm = side

Thus, side of the cube with volume 343 is 7 cm.

Volume of Cylinder

A cylinder is a three-dimensional solid that contains two parallel bases connected by a curved surface. The bases are usually circular in shape. The perpendicular distance between the bases is denoted as the height “h” of the cylinder and “r” is the radius of the cylinder.

Let’s consider some example related to the calculation of volume of cylinder.

Example 1: Calculate the volume of the cylindrical container having a radius of 4 cm and height of 35 cm. 

(Take pi = 22/7)

Solution:

Radius = 4cm

Height = 35cm

Putting the values in the formulae,

Volume of cylinder = π × 4 × 4 × 35

⇒ Volume of cylinder = π × 560 (pi = 22/7)

⇒ Volume of cylinder = 1760 cm³

Example 2: Calculate the radius of the cylinder  whose height is 21 cm and volume of the cylinder is 1100 centimeter cube?(Take pi = 22/7)

Solution:

Volume of cylinder = πr²h  cubic units

⇒ 1100 = 22/7 × r^{2 ×} 21

⇒ r² = (1100 x7) ÷ (22 x21)

⇒ r² = 7700 ÷ 462

⇒ r² = 16.66

⇒ r = √16.66

⇒ r = 4.0825

radius of the cylinder is approximately = 4.0825 cm.