# Spherical segment

Spherical segment with height h=7 has a volume V=198. Calculate the radius of the sphere of which is cut this segment.

Result

r =  3.62

#### Solution:

$h = 7 \ \\ V = 198 \ \\ \ \\ V = \dfrac{ 1 }{ 3 } \pi h^2(3r-h) \ \\ \ \\ r = \dfrac{ V }{ \pi \cdot \ h^2 } + h/3 = \dfrac{ 198 }{ 3.1416 \cdot \ 7^2 } + 7/3 \doteq 3.6196 = 3.62$

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