Spherical cap

From the sphere of radius 13 was truncated spherical cap. Its height is 6. What part of the volume is spherical cap from whole sphere?

Result

x =  13.5 %

Solution:

ρ2=132−(13−6)2=120 V1=π⋅66(3⋅ρ2+62)=1244.07 V2=4π3133=9202.77  x=V1V2 x=13.5%\rho^2 = 13^2 - (13-6)^2 = 120 \ \\ V_1 = \dfrac{ \pi\cdot 6}{6} (3\cdot \rho^2+6^2) = 1244.07 \ \\ V_2 = \dfrac{ 4 \pi}{3} 13^3 = 9202.77 \ \\ \ \\ x = \dfrac{ V_1}{ V_2} \ \\ x=13.5 \%

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