Height as diameter of base

The rotary cylinder has a height equal to the base diameter and the surface of 471 cm2. Calculate the volume of a cylinder.

Result

V =  784.801 cm3

Solution:

$S = 471 \ cm^2 \ \\ h = D \ \\ h = 2r \ \\ \ \\ S = 2 \ \pi r^2 + 2 \ \pi r h \ \\ S = 2 \ \pi r^2 + 4 \ \pi r^2 \ \\ S = 6 \ \pi r^2 \ \\ \ \\ r = \sqrt{ S/(6 \pi) } = \sqrt{ 471/(6 \cdot \ 3.1416) } \doteq 4.9987 \ cm \ \\ h = 2 \cdot \ r = 2 \cdot \ 4.9987 \doteq 9.9975 \ cm \ \\ \ \\ S_{ 1 } = \pi \cdot \ r^2 = 3.1416 \cdot \ 4.9987^2 = \dfrac{ 157 }{ 2 } = 78.5 \ cm^2 \ \\ \ \\ S_{ 2 } = 2 \cdot \ S_{ 1 } + 2 \pi \cdot \ r \cdot \ h = 2 \cdot \ 78.5 + 2 \cdot \ 3.1416 \cdot \ 4.9987 \cdot \ 9.9975 = 471 \ cm^2 \ \\ \ \\ S_{ 2 } = S \ \\ \ \\ V = S_{ 1 } \cdot \ h = 78.5 \cdot \ 9.9975 \doteq 784.801 = 784.801 \ cm^3$

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