Question

Calculate the volume of the material used in the shell to the nearest unit. The inside radius of a spherical metal shell is $2.5$ cm and the outer radius of the shell is $5$ cm.

• A. $257.91c{m}^3$
• B. $457.91c{m}^3$
• C. $417.91c{m}^3$
• D. $357.91c{m}^3$

Answer 1

The correct option is B $457.91c{m}^3$

$R=5$ cm
$r=2.5$ cm
Volume = $\frac{4}{3}\pi (R^3-r^3)$
= $\frac{4}{3}\pi (5^3-{2.5}^3)$
= $\frac{4}{3}\pi (125-15.625)$
= $\frac{4}{3}\pi \left(109.375\right)$
= $\frac{437.5\pi }{3}$
= $1312.5\pi$
= $457.91c{m}^3$