Volume of a Cylinder

Volume of a Cylinder is the amount of space enclosed inside a cylindrical shape.

• It represents how much three-dimensional space the cylinder occupies and is measured in cubic units (such as cm³, m³, etc.).
• It is calculated by multiplying the area of the circular base by the height of the cylinder.

• V = volume
• r = radius of the circular base
• h = height of the cylinder
• π ≈ 3.14

Types of Cylinders

1. Right Circular Cylinder

A right circular cylinder is a cylinder in which the base is a circle and the axis is perpendicular to the base.

Formula: V = πr²h

• r = radius of the base
• h = height

2. Oblique Cylinder

An oblique cylinder is a cylinder in which the axis is not perpendicular to the base (it is slanted).

Formula: V = πr²h

• r = radius of the base
• h = perpendicular height

3. Elliptic Cylinder

An elliptic cylinder is a cylinder whose base is an ellipse instead of a circle.

Formula: V = πabh

• a = major radius of ellipse
• b = minor radius of ellipse
  h = height

4. Right Circular Hollow Cylinder

A right circular hollow cylinder is a cylinder with an empty inner part, formed by removing a smaller cylinder from a larger one.

Formula: V = π(R² − r²)h

• R = outer radius
• r = inner radius
  h = height

Also Check

• Volume Formulas
• Volume of Cuboid
• Volume of Sphere
• Volume of Cube

Solved 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:

Given,
Volume (V) = 450 m³
Height (h) = 9 m

Formula: V = πr²h
r² = V / (πh)

r² = 450 / (3.14 × 9)
r² = 450 / 28.26
r² ≈ 15.92

r = √15.92
r ≈ 3.99 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

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 7 cm.

Q5: A hollow cylindrical tube has an outer radius of 10 cm, an inner radius of 8 cm, and a height of 30 cm. Calculate the volume of the material used to make the tube.

Answer key

1. 1848.83 cm³
2. 923.02 cm³
3.5 cm|
4. 1429.97 cm³
5. 3393.05 cm³