Question

Calculate the volume of the shell. A hollow spherical shell has inner radius $0.3$ cm and outer radius $0.5$ cm.

• A. $0.410c{m}^3$
• B. $0.310c{m}^3$
• C. $0.210c{m}^3$
• D. $0.110c{m}^3$

Answer 1

Answer: (A)

$0.410c{m}^3$

Outer radius, $R=0.5$ cm
Inner radius, $r=0.3$ cm
Volume = $\frac{4}{3}\pi (R^3-r^3)$
= $\frac{4}{3}\pi ({0.5}^3-{0.3}^3)$
= $\frac{4}{3}\pi (0.125-0.027)$
= $\frac{4}{3}\pi \left(0.098\right)$
= $\frac{0.392\pi }{3}$
= $0.13066\pi$
= $0.410c{m}^3$