Question

A solid cylinder of radius R cm and height H cm is melted and recast into smaller identical solid cylinders of height h cm and radius r cm. The number of smaller solid cylinders obtained is ______.

Options

• \[\frac{\mathrm{RH}}{r h}\]

• \[\frac{\mathrm{R}^{2} \mathrm{H}}{r^{2} h}\]

• \[\mathrm{R}^{2} \mathrm{H} \div r^{2} h^{2}\]

• \[\frac{\mathrm{RH}^{2}}{r h}\]

Answer 1

A solid cylinder of radius R cm and height H cm is melted and recast into smaller identical solid cylinders of height h cm and radius r cm. The number of smaller solid cylinders obtained is \[\underline{\boldsymbol{\frac{R^2 H}{r^2 h}}}\].

Explanation:

Given,

A solid cylinder of radius R cm and height H cm is melted and recast into smaller identical solid cylinders of height h cm and radius r cm.

Let no. of smaller cylinders formed be n.

∴ Volume of larger cylinder = n × Volume of one smaller cylinder

⇒ πR²H = n × πr²h

\[\Rightarrow n = \frac{\pi R^2 H}{\pi r^2 h} = \frac{R^2 H}{r^2 h}\]