Rotary cone

Rotary cone whose height is equal to the circumference of the base, has a volume 229 cm3.

Calculate the radius of the base circle and height of the cone.

Result

r =  3.26 cm
h =  20.51 cm

Solution:

$V = \dfrac13 \pi r^2h = 229 \ cm^3 \ \\ h = 2 \pi r \ \\ \ \\ V = \dfrac23 \pi^2r^3 \ \\ \ \\ r = \sqrt[3]{ \dfrac32 \dfrac{V}{\pi^2}} = 3.26 \ \text{ cm }$
$h = 2 \pi r = 20.51 \ \text{ cm }$

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