Question

12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. The diameter of each sphere is:

• A. $\sqrt{3}cm$
• B. $2cm$
• C. $3cm$
• D. $4cm$

Answer 1

The correct option is D

$4cm$

Volume of the cylinder$=\pi r^{2}h=\pi \times 8^2\times 2=128\pi c{m}^3$
Volume of one sphere$=\frac{Volumeofthecylinder}{12}$
$\Rightarrow \frac{4}{3}\pi r^3=\frac{128}{12}\pi \Rightarrow r^3=8\Rightarrow r=2cm$
$\therefore$ Diameter of the sphere$=4cm$