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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: Option D

Solution(By Examveda Team)

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

This Question Belongs to Arithmetic Ability >> Volume And Surface Area

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