Question

The inside radius of a spherical metal shell is $25$ cm and the thickness of the shell is $10$ cm. Calculate the volume of the material used in the shell to the nearest unit.

• A. $124,087cm$
• B. $144,087cm$
• C. $114,087cm$
• D. $134,087cm$

Answer 1

The correct option is C $114,087cm$

Thickness, $T=R-r$
$10=R-25$
$R=35$ cm
$r=25$ cm
Volume = $\frac{4}{3}\pi (R^3-r^3)$
$=$ $\frac{4}{3}\pi ({35}^3-{25}^3)$
$=$ $\frac{4}{3}\pi (42875-15625)$
$=$ $\frac{4}{3}\pi \left(27250\right)$
$=$ $\frac{109000\pi }{3}$
$=$ $114,087cm$