Question

The volume of used metal in making hemispherical shell with internal and external diameter as 8 cm and 10 cm respectively is

• A. $\frac{317\pi }{3}c{m}^3$
• B. $\frac{132\pi }{5}c{m}^3$
• C. $\frac{122\pi }{3}c{m}^3$
• D. $\frac{152\pi }{3}c{m}^3$

Answer 1

The correct option is C $\frac{122\pi }{3}c{m}^3$

Let internal and external radius of hemispherical shell be r and R respectively.

$\therefore r=\frac{8}{2}=4cm,R=\frac{10}{2}=5cm$

$\therefore$ Volume of hemispherical shell $=\frac{2}{3}\pi (R^3-r^3)$

$=\frac{2\pi }{3}(5^3-4^3)$

$=\frac{2\pi }{3}(125-64)$

$=\frac{122\pi }{3}c{m}^3$

Hence, the correct answer is option (c).