# Cylinder height

Calculate the height of the cylinder and its surface is 2500 dm2 and the bases have a diameter 5dm.

Correct result:

h =  156.655 dm

#### Solution:

$S=2500 \ \text{dm}^2 \ \\ D=5 \ \text{dm} \ \\ r=D/2=5/2=\dfrac{ 5 }{ 2 }=2.5 \ \text{dm} \ \\ \ \\ S_{1}=\pi \cdot \ r^2=3.1416 \cdot \ 2.5^2 \doteq 19.635 \ \text{dm}^2 \ \\ \ \\ S_{2}=S - 2 \cdot \ S_{1}=2500 - 2 \cdot \ 19.635 \doteq 2460.7301 \ \text{dm}^2 \ \\ \ \\ o=\pi \cdot \ D=3.1416 \cdot \ 5 \doteq 15.708 \ \text{dm} \ \\ \ \\ h=S_{2}/o=2460.7301/15.708=156.655 \ \text{dm}$

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