# Cylinder surface, volume

The area of the cylinder surface and the cylinder jacket are in the ratio 3: 5. The height of the cylinder is 5 cm shorter than the radius of the base. Calculate surface area and volume of the cylinder.

Correct result:

S =  10367.26 cm2
V =  70685.83 cm3

#### Solution:

$\dfrac{ S_1 }{ S_2 } = \dfrac35 \ \\ \dfrac{ \pi r^2 }{ 2 \pi r h } = \dfrac35 \ \\ \dfrac{ r }{ 2 h } = \dfrac35 \ \\ 5 r = 6 h \ \\ h = r-5 \ \\ \ \\ h = 25 \ cm \ \\ r = 30 \ cm \ \\ S = 2 \pi r^2 + 2 \pi r h = 2\pi\cdot 30\cdot (30+25) = 10367.26 \ \text{cm}^2 \ \\$

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