Question

Determine the volume of a spherical shell which has an inner radius of $6$ cm and an outer radius of $24$ cm.

• A. $44972c{m}^3$
• B. $56972c{m}^3$
• C. $66972c{m}^3$
• D. $56000c{m}^3$

Answer 1

The correct option is B $56972c{m}^3$

Outer radius, $R=24$ cm
Inner radius, $r=6$ cm
Volume = $\frac{4}{3}\pi (R^3-r^3)$
= $\frac{4}{3}\pi ({24}^3-6^3)$
= $\frac{4}{3}\pi (13824-216)$
= $\frac{4}{3}\pi \left(13608\right)$
= $\frac{54432\pi }{3}$
= $18144\pi$
= $56972c{m}^3$