Question

What is the volume of material that is needed to form a spherical shell whose outer radius is $5$ ft and whose inner radius is $3$ ft?

• A. $610.293f{t}^3$
• B. $510.293f{t}^3$
• C. $450.293f{t}^3$
• D. $410.293f{t}^3$

Answer 1

The correct option is D $410.293f{t}^3$

$R=5$ ft
$r=3$ ft
Volume = $\frac{4}{3}\pi (R^3-r^3)$
= $\frac{4}{3}\pi (5^3-3^3)$
= $\frac{4}{3}\pi (125-27)$
= $\frac{4}{3}\pi \left(98\right)$
= $\frac{392\pi }{3}$
= $130.666\pi$
= $410.293f{t}^3$