Question

A solid sphere of radius $3$ cm is melted and then cast into small spherical balls each of diameter $0.6$ cm. Find the number of balls thus obtained

• A. $1000$
• B. $500$
• C. $1500$
• D. $1700$

Answer 1

The correct option is A $1000$

Let the total number of balls be x.

Volume of the solid sphere

$=\frac{4}{3}\pi r^3=\frac{4}{3}\pi \times 3^{3}c{m}^3=36\pi c{m}^3$

Radius of spherical ball $=\frac{0.6}{2}cm=0.3cm$

Volume of a spherical ball

$=\frac{4}{3}\pi \times (0.3{)}^{3}c{m}^3$

$=\frac{4}{3}\pi \times \frac{3}{10}\times \frac{3}{10}\times \frac{3}{10}c{m}^3=\frac{36\pi }{1000}c{m}^3$

$\therefore$ Volume of x spherical balls

$=\frac{36\pi }{1000}xc{m}^3$

Clearly,

Volume of the solid sphere $=$ Volume of x spherical balls.

$\Rightarrow 36\pi =\frac{36\pi }{1000}x\Rightarrow x=1000$.

Hence, 1000 spherical balls are obtained by melting the given solid sphere .