Question

How many balls, each of radius $1$ cm, can be made from a solid sphere of lead of radius $8$ cm?

• A. $512$
• B. $500$
• C. $400$
• D. $345$

Answer 1

The correct option is A $512$

Volume of the spherical ball of radius 8 cm

$=\frac{4}{3}\pi \times 8^{3}c{m}^3$

Also, volume of each smaller spherical ball of radius 1 cm

$=\frac{4}{3}\pi \times 1^{3}c{m}^3$

Let n be the number of smaller balls that can be made. Then, the volume of the larger ball is equal to the sum of all the volumes of n smaller balls.

Hence, $\frac{4}{3}\pi \times n=\frac{4}{3}\pi \times 8^3$

$\Rightarrow n=8^3=512$

Hence, the required number of balls $=512$.