## Method #1 – Total Surface Area of a Cylinder from the Radius and Height

### Calculator

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

Step 1: Find the surface area of the curved part of the cylinder

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

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

Surface Area (Ends) = 2 x π x Radius^{2}

Step 3: Add the surface are of the curved part to the surface area of the ends

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

##### 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

Surface Area (Ends) = 2 x 3.14159 x 5^{2}

Surface Area (Ends) = 2 x 3.14159 x 25

Surface Area (Ends) = 157.0795

Surface Area (Total) = 471.239

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

### Calculator

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

Step 1: Find the height

Height = Volume ÷ (π x Radius^{2})

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

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

Step 3: Find the surface area of the two ends of the cylinder

Surface Area (Ends) = 2 x π x Radius^{2}

Step 4: Add the surface are of the curved part to the surface area of the ends

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

##### Example

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

Height = 785.39 ÷ (3.14159 x 5^{2})

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

Surface Area (Ends) = 2 x 3.14159 x 5^{2}

Surface Area (Ends) = 2 x 3.14159 x 25

Surface Area (Ends) = 157.0795

Surface Area (Total) = 471.239

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

### Calculator

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

Step 1: Find the radius

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

Step 3: Find the surface area of the two ends of the cylinder

Surface Area (Ends) = 2 x π x Radius^{2}

Step 4: Add the surface are of the curved part to the surface area of the ends

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

##### Example

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

Radius =√(785.39 ÷ (10 x 3.14159))

Radius =√(785.39 ÷ 31.4159)

Radius =√25

Radius = 5

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

Surface Area (Curved) = 314.159

Surface Area (Ends) = 2 x 3.14159 x 5^{2}

Surface Area (Ends) = 2 x 3.14159 x 25

Surface Area (Ends) = 157.0795

Surface Area (Total) = 314.159 + 157.0795

Surface Area (Total) = 471.239

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

### Calculator

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

Step 1: Find the radius

Radius = Area ÷ (2 x π x Height)

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

Surface Area (Ends) = 2 x π x Radius^{2}

Step 3: Add the surface are of the curved part to the surface area of the ends

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

##### 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)

Radius =314.159 ÷ 62.8318

Radius = 5

Surface Area (Ends) = 2 x 3.14159 x 5^{2}

Surface Area (Ends) = 2 x 3.14159 x 25

Surface Area (Ends) = 157.0795

Surface Area (Total) = 314.159 + 157.0795

Surface Area (Total) = 471.239

## Method #5 – Total Surface Area of a Cylinder from the Curved Surface Area and Radius

### Calculator

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

Step 1: Find the height

Height = Area ÷ (2 x π x Radius)

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

Surface Area (Ends) = 2 x π x Radius^{2}

Step 3: Add the surface are of the curved part to the surface area of the ends

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

##### 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

Surface Area (Ends) = 2 x 3.14159 x 5^{2}

Surface Area (Ends) = 2 x 3.14159 x 25

Surface Area (Ends) = 157.0795

Surface Area (Total) = 314.159 + 157.0795

Surface Area (Total) = 471.239