# Volume of a Cylinder

## Method #1 – Volume of a Cylinder from the Radius and Height

### Formula – How to find the volume of a cylinder from the radius and height

Volume = π x Radius2 x Height

##### Example

A cylinder has a radius of 5 and a height of 10

Volume = 3.14159 x 52 x 10

Volume = 3.14159 x 25 x 10

Volume = 785.3975

## Method #2 – Volume of a Cylinder from the Radius and Curved Surface Area

### Formula – How to find the volume of a cylinder from the radius and curved surface area

Step 1: Find the height of the cylinder

Height = Area ÷ (2 x π x Radius)

Step 2: Find the volume of the cylinder

Volume = π x Radius2 x Height

##### Example

A cylinder has a curved surface area of 314.159 and a radius of 5

Height = 314.159 ÷ (2 x 3.14159 x 5)

Height = 314.159 ÷ 31.4159

Height = 10

Volume = 3.14159 x 52 x 10

Volume = 3.14159 x 25 x 10

Volume = 785.3975

## Method #3 – Volume of a Cylinder from the Radius and Total Surface Area

### Formula – How to find the volume of a cylinder from the radius and total surface area

Step 1: Find the height of the cylinder

Height = (Area – (2 x π x Radius2)) ÷ (2 x π x r)

Step 1: Find the volume of the cylinder

Volume = π x Radius2 x Height

##### Example

A cylinder has a surface area of 471.24 and a radius of 5

Height = (471.24 – (2 x 3.14159 x 52)) ÷ (2 x 3.14159 x 5)

Height = (471.24 – (2 x 3.14159 x 25)) ÷ 31.4159

Height = (471.24 – 157.0795) ÷ 31.4159

Height = 314.1605 ÷ 31.4159

Height = 10

Volume = 3.14159 x 52 x 10

Volume = 3.14159 x 25 x 10

Volume = 785.3975

## Method #4 – Volume of a Cylinder from the Height and Curved Surface Area

### Formula – How to find the volume of a cylinder from the height and curved surface area

Step 1: Find the radius of the cylinder

Radius = Area ÷ (2 x π x Height)

Step 2: Find the volume of the cylinder

Volume = π x Radius2 x Height

##### Example

A cylinder has a curved surface area of 314.159 and a height of 10

Radius = 314.159 ÷ (2 x 3.14159 x 10)

Volume = 3.14159 x 52 x 10

Volume = 3.14159 x 25 x 10

Volume = 785.3975

## Method #5 – Volume of a Cylinder from the Height and Total Surface Area

### Formula – How to find the volume of a cylinder from the height and total surface area

Step 1: Find the radius of the cylinder

B = Height2 + ((2 x Area) ÷ π)

Radius = (√B – Height) ÷ 2

Step 1: Find the volume of the cylinder

Volume = π x Radius2 x Height

##### Example

A cylinder has a surface area of 471.24 and a height of 10

B = 102 + ((2 x 471.24) ÷ 3.14159)

B = 100 + (942.48 ÷ 3.14159)

B = 100 + 300

B = 400

Radius = (√400 – 10) ÷ 2

Radius = (20 – 10) ÷ 2