Method #1 – Curved Surface Area of a Cylinder from the Radius and Height
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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
Method #2 – Total Surface Area of a Cylinder from the Radius and Volume
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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
Method #3 – Curved Surface Area of a Cylinder from the Height and Volume
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Formula – How to find the curved 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
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
Method #4 – Curved Surface Area of a Cylinder from the Total Surface Area and Height
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Formula – How to find the curved surface area of a cylinder using the total surface area and height
Step 1: Find the radius
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
Radius = 10 ÷ 2
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 (Curved) = 471.239 – 157.0795
Surface Area (Curved) = 314.159
Method #5 – Curved Surface Area of a Cylinder from the Total Surface Area and Radius
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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