volume of sphere

 
 

The volume of the spherical segment is 100 cubic meter with an altitude of 8 meter. What is the volume of the sphere? Kindly show the solution. Thank you.

Radius of the sphere
$V = \dfrac{\pi h^2}{3}(3R - h)$

$100 = \dfrac{\pi (8^2)}{3}(3R - 8)$

$R = 3.164 ~ \text{m}$
 

Volume of the sphere
$V = \frac{4}{3}\pi R^3 = \frac{4}{3}\pi (3.164^3)$

$V = 132.68 ~ \text{m}^3$       answer
 

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