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Volume of a Cylinder

The volume of a cylinder is the density of the cylinder which signifies the amount of material it can carry or how much amount of any material can be immersed in it. Cylinder’s volume is given by the formula, πr2h, where r is the radius of the circular base and h is the height of the cylinder. The material could be a liquid quantity or any substance which can be filled in the cylinder uniformly. Check volume of shapes here.

Volume of cylinder has been explained in this article briefly along with solved examples for better understanding. In Mathematics, geometry is an important branch where we learn the shapes and their properties. Volume and surface area are the two important properties of any 3d shape.

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Definition

The cylinder is a three-dimensional shape having a circular base. A cylinder can be seen as a set of circular disks that are stacked on one another. Now, think of a scenario where we need to calculate the amount of sugar that can be accommodated in a cylindrical box.

In other words, we mean to calculate the capacity or volume of this box. The capacity of a cylindrical box is basically equal to the volume of the cylinder involved. Thus, the volume of a three-dimensional shape is equal to the amount of space occupied by that shape.

Volume of a Cylinder Formula

A cylinder can be seen as a collection of multiple congruent disks, stacked one above the other. In order to calculate the space occupied by a cylinder, we calculate the space occupied by each disk and then add them up. Thus, the volume of the cylinder can be given by the product of the area of base and height.

Volume of a Cylinder

For any cylinder with base radius ‘r’, and height ‘h’, the volume will be base times the height.

Therefore, the cylinder’s volume of base radius ‘r’, and height ‘h’ = (area of base) × height of the cylinder

Since the  base is the circle, it can be written as

Volume =  πr× h

Therefore, the volume of a cylinder = πr2h cubic units.

Volume of Hollow Cylinder

In case of hollow cylinder, we measure two radius, one for inner circle and one for outer circle formed by the base of hollow cylinder. Suppose, r1 and r2 are the two radii of the given hollow cylinder with ‘h’ as the height, then the volume of this cylinder can be written as;

  • V =  πh(r12 – r22)

Surface Area of Cylinder

The amount of square units required to cover the surface of the cylinder is the surface area of the cylinder. The formula for the surface area of the cylinder is equal to the total surface area of the bases of the cylinder and surface area of its sides.

  • A = 2πr2 + 2πrh

Volume of Cylinder in Litres

When we find the volume of the cylinder in cubic centimetres, we can convert the value in litres by knowing the below conversion, i.e.,

1 Litre = 1000 cubic cm or cm3
For example: If a cylindrical tube has a volume of 12 litres, then we can write the volume of the tube as 12 × 1000 cm3 = 12,000 cm3

Examples

Question 1: Calculate the volume of a given cylinder having height 20 cm and base radius of 14 cm. (Take pi = 22/7)

Solution:

Given:

Height  = 20 cm

radius = 14 cm

we know that;

Volume, V = πr2h  cubic units

V=(22/7) × 14  × 14  × 20

V= 12320 cm3

Therefore, the volume of a cylinder = 12320 cm3

Question 2: Calculate the radius of the base of a cylindrical container of volume 440 cm3. Height of the cylindrical container is 35 cm. (Take pi = 22/7)

Solution:

Given:

Volume = 440 cm3

Height = 35 cm

We know from the formula of cylinder;

Volume, V = πr2h  cubic units

So, 440 = (22/7) × r2 × 35

r= (440 × 7)/(22 × 35) = 3080/770 = 4

Therefore, r = 2 cm

Therefore, the radius of a cylinder = 2 cm.

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Frequently Asked Questions on Volume of a Cylinder

What is meant by the volume of a cylinder?

In geometry, the volume of a cylinder is defined as the capacity of the cylinder, which helps to find the amount of material that the cylinder can hold.

What is the formula for the volume of a cylinder?

The formula to calculate volume of a cylinder is given by the product of base area and its height.
Since, the base area of a cylinder is circular, we can state that
Volume of a cylinder = πr2h cubic units.

What is the volume of a hollow cylinder?

As we know, the hollow cylinder is a type of cylinder, which is empty from inside and it should possess some difference between the internal and the external radius. Thus, the amount of space occupied by the hollow cylinder in the three dimensional space is called the volume of a hollow cylinder.

How to calculate the volume of a hollow cylinder?

If R is the external radius and r is the internal radius, then the formula for calculating the cylinder’s volume is given by:
V = π (R2 – r2) h cubic units.

What is the unit for the volume of a cylinder?

The volume of a cylinder is generally measured in cubic units, such as cubic centimeters (cm3), cubic meters (m3), cubic feet (ft3) and so on.

How to find the volume of a cylinder if the diameter and height are given?

As we know, Diameter “d” = 2(Radius) = 2r.
So, r = d/2
Now, substitute the value of “r” in the volume of cylinder formula, we get
V = πr2h = π(d/2)2h
V = (πd2h)/4
Hence, the volume of the cylinder is (πd2h)/4, if its diameter and height are given.

What will happen to the cylinder’s volume if its radius is doubled?

As we know, cylinder’s volume is directly proportional to the square of its radius.
If the radius is doubled, (i.e., r = 2r), we get
V = πr2h =π(2r)2h = 4πr2h.
Hence, the cylinder’s volume becomes four times, when its radius is doubled.

What will happen to the cylinder’s volume if its radius is halved?

We know that, the volume of cylinder ∝ Radius2
Thus, if radius is halved, (i.e., r = r/2), we get
V = π(r/2)2h = (πr2h)/4
Therefore, the cylinder’s volume becomes 1/4th, if its radius is halved.

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