Question

Find the volume of material that is needed to form a spherical shell whose outer radius is $3.0$ inches and whose inner radius is $0.1$ inches.

• A. $103.035i{n}^3$
• B. $93.035i{n}^3$
• C. $123.035i{n}^3$
• D. $113.035i{n}^3$

Answer 1

The correct option is D $113.035i{n}^3$

$R=3.0$ in
$r=0.1$ in
Volume = $\frac{4}{3}\pi (R^3-r^3)$
= $\frac{4}{3}\pi (3^3-{0.1}^3)$
= $\frac{4}{3}\pi (27-0.001)$
= $\frac{4}{3}\pi \left(26.999\right)$
= $\frac{107.996\pi }{3}$
= $35.998\pi$
= $113.035i{n}^3$