Question

If a solid metallic sphere of radius $8$ cm is melted and recasted into $n$ spherical solid balls of radius $1$ cm, then $n$ is:

• A. $500$
• B. $510$
• C. $512$
• D. $516$

Answer 1

The correct option is C $512$

Volume of sphere$=\frac{4}{3}\pi r^3$

For solid metallic sphere $radius\left(r\right)=8cm$

$\therefore Volume=\frac{4}{3}\times 3.14\times 8^3$

$=\frac{4}{3}\times 3.14\times 512$

$=\frac{6430.72}{3}$

$=2143.57c{m}^3$

For spherical solid balls $radius\left(R\right)=1cm$

$\therefore Volume=\frac{4}{3}\times 3.14\times 1^3$

$=\frac{4}{3}\times 3.14\times 1$

$=\frac{12.56}{3}$

$=4.186c{m}^3$

In order to find the number of balls carved from larger sphere we need to divide the larger ball to small ball

$\therefore \frac{2143.57}{4.186}=512.08\approx 512balls$