# Cylinder surface area

Volume of a cylinder whose height is equal to the radius of the base is 678.5 dm3. Calculate its surface area.

Result

S =  452.352 dm2

#### Solution:

$V = 678.5 \ \\ h = r \ \\ V = \pi r^2 \ h = \pi r^3 \ \\ r = \sqrt[3]{ V/\pi} = \sqrt[3]{ 678.5/3.1416} \doteq 5.9998 \ \\ h = r = 5.9998 \doteq 5.9998 \ \\ S = 2 \pi \cdot \ r^2 + 2 \pi \cdot \ r \cdot \ h = 2 \cdot \ 3.1416 \cdot \ 5.9998^2 + 2 \cdot \ 3.1416 \cdot \ 5.9998 \cdot \ 5.9998 \doteq 452.352 = 452.352 \ dm^2$

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