Question

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

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

Answer 1

The correct option is D

$4cm$

Given diameter of the cylinder = 16 cm $\Rightarrow R=8cm$
Volume of the cylinder of radius $R$ and height $h$
$=\pi R^2\times h=\pi \times 8^2\times 2=128\pi c{m}^3$
As this volume is filled into 12 identical spheres, Volume of one sphere$=\frac{Volumeofthecylinder}{12}$

Let the radius of the sphere be $r$
$\Rightarrow \frac{4}{3}\pi r^3=\frac{128}{12}\pi \Rightarrow r^3=8\Rightarrow r=2cm$
$\therefore$ diameter of the sphere$=4cm$