Question

A solid cylinder of iron, the radius of whose base is $2$ cm and height $9$ cm, is melted and turned into sphere. The radius of the sphere so formed is

• A. $6$ cm
• B. $5$ cm
• C. $4$ cm
• D. $3$ cm

Answer 1

Answer: (D)

$3$ cm

Volume of sphere=volume of cylinder

$\Rightarrow \frac{4}{3}\pi R^3=\pi r^{2}h\Rightarrow \frac{4}{3}{R}^3=2\times 2\times 9\Rightarrow R^3=\frac{2\times 2\times 9\times 3}{4}=27$

$\Rightarrow R=\sqrt[3]{327}=3cm$

$\therefore$ Radius of sphere$=3cm$