Question

A metallic ball of radius 18 cm is melted to form a certain number of smaller metallic balls of radius 6 cm each. Find the number of such balls.

• A. 1
• B. 3
• C. 5
• D. 6

Answer 1

The correct option is D

6

Since the metallic ball is converted into smaller metallic balls, the volume must remain constant.
Let 'n' be the total number of the smaller metallic balls.

Note that the volume of n number of smaller balls = Volume of the big metallic ball

$n\times \frac{4}{3}\pi (6{)}^3=\frac{4}{3}\pi (18{)}^3$

$\Rightarrow n=\frac{18\times 18\times 18}{6\times 6\times 6}$

$\Rightarrow n=27$

Hence, there are 27 such small metallic balls.