Question

A lead ball of radius $24$ cm is melted down and recast into smaller balls of radius $6$ cm. Assuming that no metal is lost in this process, number of complete smaller balls that can be made, is -

• A. $4$
• B. $16$
• C. $36$
• D. $64$

Answer 1

Answer: (D)

$64$

Volume of large ball $=\frac{4}{3}\pi r^3$

$=\frac{4}{3}\times \pi \times 24\times 24\times 24$

$=18432\pi {cm}^3$

Volume of 1smaller ball $=\frac{4}{3}\times \pi \times 6\times 6\times 6$

$=288\pi {cm}^3$

$\therefore$ Number of small balls $=\frac{Volumeoflargeball}{Volumeof1smallball}$

$=\frac{18432\pi }{288\pi }=64$