Question

If the height of a cylinder is doubled, what should be the radius of the base so that the resulting cylinder has the same volume as the original cylinder? (Take height and radius of the original cylinder as h and r respectively).

• A. 4
• B. 2
• C. $\frac{1}{\sqrt{2}}$
• D. $\frac{1}{2}$

Answer 1

The correct option is C

$\frac{1}{\sqrt{2}}$

Let r b the radius and h be the height then

volume = $\pi r^2$ h

If height is doubled and volume is same

and let x be radius then $\pi r^{2}h=\pi (x{)}^2\times 2h$

$i.e.,\pi (x{)}^2\times 2h=\pi r^{2}h$

$\Rightarrow 2x^2=r^2$

$\Rightarrow x^2=\frac{1}{2}{r}^2={\left(\frac{1}{\sqrt{2}}r\right)}^2$

$\therefore$ Radius = $\frac{1}{\sqrt{2}}r$