Method #1 – Total Surface Area of a Cylinder from the Radius and Height
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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 Radius2
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 52
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
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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 Radius2)
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 Radius2
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 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
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 (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 Radius2
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 52
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 Radius2
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 52
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 Radius2
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 52
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