# Curved Surface Area of a Cylinder

## Formula – How to find the curved surface area of a cylinder using the height and radius

Surface Area (Curved) = 2 x π x Radius x Height

Step 2: Find the surface area of the two ends of the cylinder

##### Example

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

Surface Area (Curved) = 2 x 3.14159 x 5 x 10

Surface Area (Curved) = 314.159

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

Step 1: Find the height

Height = Volume ÷ (π x Radius2)

Step 2: Find the surface area of the curved part of the cylinder

Surface Area (Curved) = 2 x π x Radius x Height

##### Example

A cylinder has a volume of 785.39 and a radius of 5

Height = 785.39 ÷ (3.14159 x 52)

Height = 785.39 ÷ (3.14159 x 25)

Height = 785.39 ÷ 78.53975

Height = 10

Surface Area (Curved) = 2 x 3.14159 x 5 x 10

Surface Area (Curved) = 314.159

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

Radius =√(Volume ÷ (Height x π))

Step 2: Find the surface area of the curved part of the cylinder

Surface Area (Curved) = 2 x π x Radius x Height

##### Example

A cylinder has a volume of 785.39 and a height of 10

Radius =√(785.39 ÷ (10 x 3.14159))

Surface Area (Curved) = 2 x 3.14159 x 5 x 10

Surface Area (Curved) = 314.159

## Formula – How to find the curved surface area of a cylinder using the total surface area and height

B = Height2 + ((2 x Area) ÷ π)

Radius = (√B – Height) ÷ 2

Step 2: Find the surface area of the two ends of the cylinder

Surface Area (Ends) = 2 x π x Radius2

Step 3: Subtract the surface area of the two ends of the cylinder from the total surface area

Surface Area (Curved) = Surface Area (Total) – Surface Area (Ends)

##### Example

A cylinder has a total surface area of 471.239 and a height of 10

B = 102 + ((2 x 471.239) ÷ 3.14159)

B = 100 + (942.478 ÷ 3.14159)

B = 100 + 300

B = 400

Radius = (√400 – 10) ÷ 2

Radius = (20 – 10) ÷ 2

Surface Area (Ends) = 2 x 3.14159 x 52

Surface Area (Ends) = 2 x 3.14159 x 25

Surface Area (Ends) = 157.0795

Surface Area (Curved) = 471.239 – 157.0795

Surface Area (Curved) = 314.159

## Formula – How to find the curved surface area of a cylinder using the total surface area and radius

Step 1: Find the height

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

Step 2: Find the surface area of the two ends of the cylinder

Surface Area (Ends) = 2 x π x Radius2

Step 3: Subtract the surface area of the ends of the cylinder from the total area of the cylinder

Surface Area (Curved) = Surface Area (Total) – Surface Area (Ends)

##### Example

A cylinder has a total surface area of 471.239 and a radius of 5

Height =(471.239 – (2 x 3.14159 x 52)) ÷ (2 x 3.14159 x 5)

Height =(471.239 – (2 x 3.14159 x 25)) ÷ 31.4159

Height = (471.239 – 157.0795) ÷ 31.4159

Height = 314.1595 ÷ 31.4159

Height = 10

Surface Area (Ends) = 2 x 3.14159 x 52

Surface Area (Ends) = 2 x 3.14159 x 25

Surface Area (Ends) = 157.0795

Surface Area (Curved) = 471.239 – 157.0795

Surface Area (Curved) = 314.159