Question

A spherical lead ball of radius $10\mathrm{cm}$ is melted and small lead balls of radius $5\mathrm{mm}$ are made. The total number of possible small lead balls is

• A. $800$
• B. $125$
• C. $400$
• D. $8000$

Answer 1

The correct option is D

$8000$

Calculating the number of small lead balls

radius of spherical lead ball$=10cm$

radius of $n$small lead balls$=5mm=\frac{5}{10}cm=0.5cm$

Number of possible small lead balls made, $n=?$

Volume of sphere$=\frac{4}{3}{\mathrm{\pi r}}^3$

The volume of spherical lead ball$=n\times$Volume of one small lead ball

$$\begin{gathered} \Rightarrow \frac{1}{3}\pi {\left(10\right)}^3=n\times \frac{1}{3}\mathrm{\pi }{(0.5)}^3 \\ 1000=\mathrm{n}\times 0.125 \\ n=\frac{1000}{0.125}=8000 \end{gathered}$$

Therefore, the number of small lead balls will be $8000$

Hence, option D is correct.