Question

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

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

Answer 1

Answer: (B)

$1000$

Radius of bigger ball $R=6cm$

Radius of smaller balls $r=\frac{1.2}{2}=0.6cm$

Volume of bigger ball $V_1=\frac{4}{3}\pi R^3$

$=\frac{4}{3}\times \frac{22}{7}\times 6^3$

$=905.14$

Volume of smaller ball $V_2=\frac{4}{3}\pi R^3$

$=\frac{4}{3}\times \frac{22}{7}\times (0.6{)}^3$

$=0.91514$

Number of balls $=\frac{V_1}{V_2}$

$=\frac{905.14}{0.90514}$

$=1000$