Question

The diameter of a solid metallic sphere is $16$ cm. The sphere is melted and recast into $8$ equal solid spherical balls. Determine the radius of the ball.

Answer 1

Volume of the Spheec $=\frac{4}{3}\pi \times r^3$

$=\frac{4}{3}\pi \times {\left(\frac{16}{2}\right)}^3$

but r br the radius of the ball

$8\times \frac{4}{3}\pi \times r^3=\frac{4}{3}\pi \times 8^3$

$\Rightarrow 8r^3=8^3$

$\Rightarrow r^3=8^2=(2^3{)}^2$

$\Rightarrow r^3=(2^2{)}^3=4^3$

$\therefore r=4cm$

Hence radius of the ball = 4 cm