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.

Engineering Mathematics

August 22, 2015 - 11:56am

#1
The volume of the spherical segment is 100 cubic meter with an altitude of 8 meter. What is the volume of the 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