# 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?

Correct result:

x =  13.5 %

#### Solution:

$\rho^2 = 13^2 - (13-6)^2 = 120 \ \\ V_1 = \dfrac{ \pi\cdot 6}{6} (3\cdot \rho^2+6^2) = 1244.07 \ \\ V_2 = \dfrac{ 4 \pi}{3} 13^3 = 9202.77 \ \\ \ \\ x = \dfrac{ V_1}{ V_2} \ \\ x=13.5 \%$

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