Question

A solid sphere of radius 6 cm is melted and recast into small spherical balls each of diameter 1.2 cm. Find the number of balls, thus obtained.

• A. $100$
• B. $1000$
• C. $2000$
• D. None of these

Answer 1

The correct option is B $1000$

Given diameter of the spherical ball $=1.2\text{cm}$

So, the radius is $=\frac{1.2}{2}=0.6\text{cm}$

Volume of the large sphere $=\frac{4}{3}\pi R^3=\frac{4}{3}\times \frac{22}{7}\times 6\times 6\times 6$

Volume of one spherical ball $=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times 0.6\times 0.6\times 0.6$

Number of small balls is given by dividing the volume of the large sphere with the volume of one spherical ball, i.e.,

Number of small balls $=\frac{\frac{4}{3}\times \frac{22}{7}\times 6\times 6\times 6}{\frac{4}{3}\times \frac{22}{7}\times 0.6\times 0.6\times 0.6}=1000$