A hollow spherical metallic ball has an external diameter 6 cm and is $$\frac{1}{2}$$ cm thick. The volume of metal used in the ball is :
a) $$37\frac{2}{3}{\text{ c}}{{\text{m}}^3}$$
b) $$40\frac{2}{3}{\text{ c}}{{\text{m}}^3}$$
c) $$41\frac{2}{3}{\text{ c}}{{\text{m}}^3}$$
d) $$47\frac{2}{3}{\text{ c}}{{\text{m}}^3}$$

Answer: d
Explanation: External radius = 3 cm
Internal radius = (3 – 0.5) cm = 2.5 cm
Volume of the metal :
$$\eqalign{ & = \left[ {\frac{4}{3} \times \frac{{22}}{7} \times \left\{ {{{\left( 3 \right)}^3} – {{\left( {2.5} \right)}^3}} \right\}} \right]{\text{ c}}{{\text{m}}^3} \cr & = \left( {\frac{4}{3} \times \frac{{22}}{7} \times \frac{{91}}{8}} \right){\text{ c}}{{\text{m}}^3} \cr & = \left( {\frac{{143}}{3}} \right){\text{ c}}{{\text{m}}^3} \cr & = 47\frac{2}{3}{\text{ c}}{{\text{m}}^3} \cr} $$