Question

A spherical shell 2 m thick has an outer diameter of 12 m. Find the volume of the material of which it is made.

• A. $232.66\pi m^3$
• B. $212.66\pi m^3$
• C. $202.66\pi m^3$
• D. $242.66\pi m^3$

Answer 1

The correct option is C $202.66\pi m^3$

R $=\frac{Diameter}{2}$

$=\frac{12}{2}=6$m
$r=R-2=6-2=4m$
Volume $=\frac{4}{3}\pi (R^3-r^3)$
$=\frac{4}{3}\pi (6^3-4^3)$

$=\frac{4}{3}\pi (6^3-4^3)$

$=\frac{4}{3}\pi (216-64)$

$=\frac{4}{3}\pi \left(152\right)$

$=\frac{608\pi }{3}$

$=202.66\pi m^3$