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Volume of a Cylinder: Formula, Definition and Examples

Last Updated : 02 May, 2024
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Volume of a Cylinder is defined as the space occupied by the Cylinder. Formula for the volume of a cylinder is equal to πr2h where r is the radius of the base and h is the height of the cylinder. A cylinder is a 3-dimensional solid figure with two identical bases connected by a curving surface.

Volume-of-Cylinder

Volume of Cylinder

Now learn about the Volume of a Cylinder Definition, the Formula, and How to Calculate the Volume of a Cylinder with solved examples.

What is Cylinder?

Cylinder in mathematics is defined as any that has two circular bases and a curved surface that connects them. For example, Gas cylinders and Rolling Pin in our houses resemble cylindrical shapes.

Cylinder Definition

Cylinder is defined as a 3-D figure in which the base are circle and both surfaces are connected by a curved surface.

Volume of Cylinder

Volume of a cylinder is the total capacity of any cylinder, i.e. the total amount of liquid any cylinder can hold. It is generally measured in liters, volume can also be measured in m3, cm3, etc. Volume of Cylinder is calculated by multiplying area of circular base (πr2) of cylinder by its height (h).

Volume of Cylinder Formula

Volume of Cylinder is equal to πr2h. Where, r is the radius of radius of the base and h is the height of the cylinder.

VCylinder = πr2h

Volume of Solid Cylinder

Volume of a cylinder is also equal to the amount of space taken by it in a three-dimensional space. In other words, it determines the space or region enclosed by the cylinder is its volume, and the unit of volume is cubic unit i.e., the number of unit cubes (cubes of unit length) that may fit into an object.

Volume of Cylinder equation V = πr2h is also called Volume of Cylinder Equation.

Volume of a Cylinder

Volume of Cylinder

Volume of a Right Circular Cylinder

In a Right Circular Cylinder angle between the plane of the base or top and the curved surface is a right angle. For a right circular cylinder, the base is a circle with radius r, thus its area is πr2, and the height of the cylinder is h then the volume of the cylinder is: 

Volume of a Right Circular Cylinder

Volume of Right Circular Cylinder

Volume of a Hollow Cylinder

A hollow cylinder is a cylinder that is hollow from the inside thus, its bases form a ring with two radii inner radius and an outer radius. Suppose a hollow cylinder is taken with its inner radius as r and outer radius as R and the height of the cylinder is h then volume of hollow cylinder is given as:

Volume of a Hollow Cylinder

Volume of a Hollow Cylinder

Volume of an Oblique Cylinder

In an Oblique Cylinder angle between the plane of the base or top and the curved surface is not a right angle, but volume is given by the same formula as a product of the area of the base and the height of the cylinder. 

Volume of an Oblique Cylinder

Volume of Oblique Cylinder

Volume of an Elliptic Cylinder

A cylinder; with an ellipse as its base instead of a circle, is known as Elliptic Cylinder. Let both radii of the base which is an ellipse be a and b and the height of the cylinder be h, then

Volume of an Elliptic Cylinder

Volume of Elliptic Cylinder

How To Calculate Volume of a Cylinder?

Let’s take an example to understand how we can calculate the volume of a cylinder.

Example: Calculate the volume of a cylinder of radius 4 m and height 5 m.

Step 1: Note the radius and height of cylinder. In this example, the radius of the cylinder is 4 m and height is 5 m.

Step 2: We know that the volume of a cylinder is equal to πr2h. Substitute the given value of radius and height in the formula.

Step 3: So, the volume of cylinder is calculated as, 3.14 × (4)2 × 5 = 251.20 cu. m.

Volume of Cylinder in Liters

Generally, the volume of a cylinder is calculated in cubic meters or cubic centimetres but we can change them in litres by using the conversion discussed below i.e.,

1 cm3 = 1 ml

1000 cm3 = 1 litre

1 m3 = 1000000  cm3 = 1000 litres

Example: If a cylinder has a volume of 32 m3 it can be written as 32×1000 litres = 32000 litres

Formulas of Cylinder

Some formulas for cylinder other than volume formulas are,

Surface Area of a Cylinder

Surface Area of any figure is defined as the area required to totally cover the surface of any object. So, the surface area of a cylinder can be defined as the area required to cover the surface of the cylinder. 

CSA of a Cylinder

Curved Surface Area or CSA is the area of the surface that is not flat but rounded. So, the CSA of the cylinder is all the surface except the base and top. If r is the radius of the base and h is the height of the cylinder, then CSA is given as follows:

CSA of Cylinder = 2πrh

TSA of a Cylinder

Total Surface Area or TSA is the area of the completer surface of the cylinder. So, TSA is the sum of the CSA and the area of the top as well as the base of the cylinder. So, if the base radius of the cylinder is r and the height of the cylinder is h then TSA is given by,

TSA of Cylinder = 2πr(r+h)

Volume of a Cylinder

Volume of a cylinder is the space occupied by the cylinder and if we take a cylinder of radius ‘r’ and height ‘h’ then its volume is calculated by the formula:

Volume of Cylinder = πr2h

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Volume of Cylinder Examples

Example 1: Calculate the volume of a cylinder of radius 3 m and a height of 4 m. (take π = 3.14)

Solution:

We have, r = 3 and h = 4

Using the formula we have,

V = πr2h

⇒ V = 3.14 × (3)2 × 4 

⇒ V = 113.04 m3

Example 2: Calculate the volume of a cylinder of radius 4 m and a height of 7 m.

Solution:

We have, r = 4 and h = 7

Using the formula we have,

V = πr2h

⇒ V = 3.14 × (4)2 × 7

⇒ V = 351.68 m3

Example 3: Calculate the radius of a cylinder if its volume is 300 m3 and height is 7 m.

Solution:

We have, V = 300 and h = 7

Using the formula we have,

V = πr2h

⇒ r2 = V/πh

⇒  r2 = 300/(3.14 × 7)

⇒  r = 3.68 m

Example 4: Calculate the radius of a cylinder if its volume is 450 m3 and its height is 9 m.

Solution:

We have, V = 450 and h = 9

Using the formula we have,

V = πr2h

⇒ r2 = V/πh

⇒ r2 = 450/(3.14 × 9)

⇒ r = 12.52 m

Example 5: Calculate the height of a cylinder if its volume is 570 m3 and its radius is 4 m.

Solution:

We have, V = 570 and r = 4

Using the formula we have,

V = πr2h

⇒ h = V/πr2

⇒ h = 570/(3.14 × 4 × 4)

⇒ h = 11.34 m

Example 6: Calculate the height of a cylinder if its volume is 341 m3 and its radius is 6 m.

Solution:

We have,

V = 341 m3

r = 6 m

Using the formula we have,

V = πr2h

⇒ h = V/πr2

⇒ h = 341/(3.14 × 6 × 6)

⇒ h = 3.01 m

Practice Questions on Volume of Cylinder

Q1: Find Volume of Cylinder whose diameter is 14 cm and height is 12 cm.

Q2: Find Volume of Cylinder whose surface area of base is 84 cm2 and height is 11 cm.

Q3: Find the height of cylinder whose radius is 7 cm and volume is 770 cm3

Q4: Find the volume of a hollow cylinder of height 13 cm whose inner radius is 6 cm and outer radius is 1 cm.

Volume of Cylinder – FAQs

What is Volume of a Cylinder?

Volume of a cylinder is defined as the capacity of the cylinder, i.e. the amount of substance a cylinder can hold. It can also be defined as the total material required for making a cylinder.

What is Formula for the Volume of a Cylinder?

Volume of the cylinder (V) is given by the formula, V = (Area of Circular Base) × (Height) Or V = πr2h

What is Volume of a Cylinder if its Radius is Doubled?

As the volume of the circle is proportional to the square of the radius. So if the radius of the circle is doubled then its volume becomes four times.

What is Volume of Cylinder if its Radius is halved?

As the volume of the circle is proportional to the square of the radius. So if the radius of the circle is halved then its volume becomes one by four times.

What is unit of Volume of a Cylinder?

Volume of a cylinder is measured in cubic units, i.e. cubic centimeters (cm3), cubic meters (m3), cubic feet (ft3) and so on for mathematical purposes. In general usage, it is also measured in Litters (l), milliliters (ml), etc.

What is 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 Volume of an Oblique Cylinder?

Formula to find the volume of an oblique cylinder is same as the volume of the cylinder and the volume of the oblique cylinder is calculated using the formula. V = π r2 h cubic units.

What is Volume of an Elliptical Cylinder?

Formula to find the volume of an Elliptical Cylinder is, V = πabh cubic units. Where, a and b are the radii of bases of the cylinder and h is the height of the cylinder.

What is Volume of a Solid Cylinder?

Volume of Solid Cylinder is the volume of material used in making the cylinder. For any solid cylinder of height ‘h’ and radius ‘r’ its volume is given by the formula, V = πr2h.



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