# Cylinder and its circumference

If the height of a cylinder is 4 times its circumference. What is the volume of the cylinder in terms of its circumference, c?

Result

V = (Correct answer is: c^3 / pi)

#### Solution:

$h = 4c \ \\ c = 2 \ \pi r \ \\ \ \\ S_{ 1 } = \pi r ^2 = \pi (c/(2 \ \pi))^2 \ \\ S_{ 1 } = c^2 / (4 \ \pi) \ \\ \ \\ V = S_{ 1 } \ h = (c^2 / (4 \ \pi)) \cdot \ (4c) = \dfrac{ c^2 \cdot \ 4 \ c }{ 4 \ \pi } \ \\ \ \\ V = \dfrac{ c^3 }{ \pi } \ \\ \ \\ V = c^3 / \pi = c^3 / 3.1416$

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