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Volume of a Cylinder

In this section, we will learn the formula of the volume of a cylinder and how to find the volume of a cylinder along with proper examples.

A cylinder is a 3D geometrical shape with the two-circular base. It has two circular bases, one at top and the other at the bottom. We can also define a cylinder as an arrangement of circular disks in stacked form. There are two types of cylinders:

  • Cylinder or Solid Cylinder
  • Hollow Cylinder
Volume of a Cylinder

Definition

The number of cubic units that will exactly fill a cylinder is called the volume of the cylinder. In other words, the space covered by a cylinder is called the volume of a cylinder.

The Volume of Cylinder Formula

It is the product of the area of base and height of the cylinder.

V=πr2 h

Volume of a Hollow Cylinder

A cylinder that is hollow from inside is called a hollow cylinder. There are two radii in the hollow cylinder. One for the inner cylinder and the other for an outer cylinder formed by the base.

Suppose, r1 is the radius of the outer circle, r2 is the radius of the inner circle, and h is the height of the cylinder, then the volume of the hollow cylinder will be:

Volume of a Cylinder

How to Find Volume of a Cylinder

We can find the volume of a cylinder by multiplying the area of a circle by the height of the cylinder.

Volume of a Cylinder

We know the formula of the area of a circle:

The Area of a Circle (A)= πr2

Multiply the area of a circle by the height of the cylinder, we get the volume of the cylinder. Since,

The Volume of a Cylinder (V)= πr2 h

Where:

π: It is a constant whose value is 3.142 or 22/7.

r: It is the radius of the cylinder.

h: It is the height of the cylinder.

Note: The radius and height must be in the same unit. Convert the units if they are different.

Unit of Volume

The unit of the volume is a cubic unit or unit3. For example, if the radius and height are given in centimeters, the volume will also in centimeters, and the unit will be cubic centimeters or cm3.

Let's see some examples.

Example 1: The radius of a cylinder is 5 cm, and the height is 12 cm. Calculate the volume of the cylinder. Take π=Volume of a Cylinder.

Solution:

Given, radius (r) = 5 cm

Height (h) = 12 cm

π=Volume of a Cylinder

Volume (V) =?

Volume of a Cylinder

We know the formula of volume of a cylinder:

V= πr2 h

Putting the values in the above formula, we get:

Volume of a Cylinder

Hence, the volume of the cylinder is 942.85 cm3.

Example 2: Calculate the volume of a cylinder whose radius is 3 cm and the height is 6 cm. (π=3.14)

Solution:

Given, radius (r) = 3 cm

Height (h) = 6 cm

π=3.14

Volume (V) =?

Volume of a Cylinder

We know the formula of volume of a cylinder:

V= πr2 h

Putting the values in the above formula, we get:

V=3.14×(32)×6
V=3.14×9×6
V=3.14×54
V=169.56

Hence, the volume of the cylinder is 169.56 cm3.

Example 3: What is the volume of the cylinder given below.

Volume of a Cylinder

Solution:

Given, radius (r) = 4.5 cm

Height (h) = 8 cm

Volume (V) =?

We know the formula of volume of a cylinder:

V= πr2 h

Putting the values in the above formula, we get:

V=3.14×(4.52)×8
V=3.14×20.25×8
V=508.68

Hence, the volume of the cylinder is 508.68 cm3.

Example 4: The volume of a cylinder is 255 cm3 and the height is 15 cm. Find the radius (r) of the cylinder.

Solution:

Given, Volume (V) = 255 cm3

Height (h) = 15 cm

π=3.14

Radius (r) =?

We know the formula of volume of a cylinder:

V= πr2 h

Putting the values in the above formula, we get:

Volume of a Cylinder

Hence, the radius of the cylinder is 2.3 cm.

Example 5: Find the volume of the hollow cylinder.

Volume of a Cylinder

Solution:

Given, radius of outer cylinder (r1) = 2.4 cm

radius of inner cylinder (r2) = 2 cm

Height (h) = 10 cm

π=3.14

Volume (V) =?

We know the formula of volume of the hollow cylinder:

Volume of a Cylinder

Putting the values in the above formula, we get:

V=3.14×10×(2.42-22)
V=3.14×10×(5.76-4)
V=3.14×10×(1.76)
V=55.264

Hence, the volume of the hollow cylinder is 55.264 cm3.

Example 6: The outer and inner radius of a pipe is 8 and 6 cm, respectively. The height of the pipe is 15 cm. Find the volume of the pipe. Take pi=3.14.

Solution:

Given, radius of outer cylinder (r1) = 8 cm

radius of inner cylinder (r2) = 6 cm

Height (h) = 15 cm

π=3.14

Volume (V) =?

Volume of a Cylinder

We know the formula of volume of the hollow cylinder:

Volume of a Cylinder

Putting the values in the above formula, we get:

V=3.14×15×(82-62)
V=3.14×15×(64-36)
V=3.14×15×2
V=1318.8

Hence, the volume of the hollow cylinder is 1318.8 cm3.


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