# Volume and surface

Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm2.

Result

V =  19.15 dm3
S =  40 dm2

#### Solution:

$24 = 2 \pi rh \ \\ \ \\ h:D = 3:4 \ \\ h:r = 3:2 \ \\ 2h = 3r \ \\ 24 = 3 \pi r^2 \ \\ r = \sqrt{ 8 / \pi } = 1.596 \ dm \ \\ h = \dfrac32 r = 2.394 \ dm \ \\ V = \pi r^2 h = 19.15 \ dm^3$
$S = 24 + 2 \pi r^2 = 40 \ dm^2$

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