Question

The volume of a hemispherical shell of outer radius 7 cm and inner radius 3.5 cm is

• A. $707\pi c{m}^3$
• B. $767\pi c{m}^3$
• C. $\frac{2401\pi }{12}c{m}^3$
  
• D. $266.75\pi c{m}^3$

Answer 1

The correct option is C $\frac{2401\pi }{12}c{m}^3$


Let $r_1$ and $r_2$ be the outer and inner radius of hemispherical shell, respectively.
$\therefore r_1=7cm$ and $r_2=3.5cm$
Volume of hemispherical shell
$=\frac{2}{3}\pi (r_1^3-r_2^3)$
$=\frac{2}{3}\times \pi \left[\right(7{)}^3-{\left(\frac{7}{2}\right)}^3]$
$=\frac{2}{3}\times \pi \times 7^3\times (1-\frac{1}{8})$
$=\frac{2}{3}\times \pi \times 343\times \frac{7}{8}$
$=\frac{2401}{12}\pi c{m}^3$
Hence, the correct answer is option (c).