# Diameter = height

The surface of the cylinder, the height of which is equal to the diameter of the base, is 4239 cm square. Calculate the cylinder volume.

Result

V =  21189.627 cm3

#### Solution:

$S=4239 \ \text{cm}^2 \ \\ D=h=2r \ \\ \ \\ S=2 \ \pi r^2 + 2 \ \pi r h=2 \ \pi r (r+h) \ \\ S=2 \ \pi r (r+2r)=2 \ \pi r 3r=6 \ \pi r^2 \ \\ \ \\ r=\sqrt{ \dfrac{ S }{ 6 \pi } }=\sqrt{ \dfrac{ 4239 }{ 6 \cdot \ 3.1416 } } \doteq 14.9962 \ \text{cm} \ \\ h=2 \cdot \ r=2 \cdot \ 14.9962 \doteq 29.9924 \ \text{cm} \ \\ \ \\ V=\pi \cdot \ r^2 \cdot \ h=3.1416 \cdot \ 14.9962^2 \cdot \ 29.9924 \doteq 21189.6268 \doteq 21189.627 \ \text{cm}^3$

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