Question

The inner diameter of the spherical shell is $12$ mm and outer diameter is $24$ mm. Find the volume of the shell.

• A. $4330m{m}^3$
• B. $6330m{m}^3$
• C. $5330m{m}^3$
• D. $3330m{m}^3$

Answer 1

Answer: (B)

$6330m{m}^3$

Outer radius, $R=12$ mm
Inner radius, $r=6$ mm
Volume = $\frac{4}{3}\pi (R^3-r^3)$
= $\frac{4}{3}\pi ({12}^3-6^3)$
= $\frac{4}{3}\pi (1728-216)$
= $\frac{4}{3}\pi \left(1512\right)$
= $\frac{6048\pi }{3}$
= $2016\pi$
= $6330m{m}^3$