Spherical segment

Spherical segment with height h=5 has a volume V=117. Calculate the radius of the sphere of which is cut this segment.

Correct result:

r =  3.16

Solution:

h=5 V=117  V=13πh2(3r−h)  r=Vπ⋅ h2+h/3=1173.1416⋅ 52+5/3=3.16h=5 \ \\ V=117 \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \pi h^2(3r-h) \ \\ \ \\ r=\dfrac{ V }{ \pi \cdot \ h^2 } + h/3=\dfrac{ 117 }{ 3.1416 \cdot \ 5^2 } + 5/3=3.16

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