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Circumference, Area,
Surface Area, and Volume
By Taylor Winter
Derive the Formula:
Surface area of a Cylinder
Example Problems
1. A can of soup has a height of 4 in. and a radius of 3 in. What is the surface area of that can?
Area of a circle= πr^2
r= 3 in.
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π3 in. ^2= 9π in.^2
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Area of a rectangle= b x h
b= circumference h= 4 in.
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Circumference= 2πR
r= 3 in.
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2 x π x 3 in.= 6π in.= b
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6π in^2 x 4 in^2= 24π in^2
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2(base) + 1( lateral face)=
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(2 x 9π in^2) + 24π in^2= 18π in^2 + 24π in^2= 42π in^2
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The surface area of the soup can is 42π in^2.
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To find the surface area of a cylinder you have to draw a net of the shape. From there you find the area of each shape and then add them together.
Generally, it will be 2 base shapes and then 1 lateral face.
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The length of the lateral face is equal to the circumference of the base shape.
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