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# The lateral surface area of a cylinder

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The lateral surface area of a cylinder is 80% of its surface area. What is the ratio between the base radius and the height of the cylinder?

Nov 15, 2020

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The total surface area is ( 2* pi *  r ) ( r  + h)

The lateral surface area is (2 * pi * r ) * h  =  .80  ( 2 * pi * r) ( r + h)

Divide out 2* pi * r  from both sides and we have that

h  = .80 ( r + h)   simplify

h = .80r + .80h

h - .80 h =  .80r

.20 h  = .80 r     divide both sides by .80

(1/4) h =  r       divide  both sides by h

(1/4)  = r / h        [ the base radius is 1/4 the height ]

Nov 15, 2020
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