Question

If the height of a cylinder is doubled, by what number must the radius of the base be multiplied so that the resulting cylinder has the same volume as the original cylinder ?

(a) 4 (b) $\frac{1}{\sqrt{2}}$

(c) 2 (d) $\frac{1}{2}$

Answer 1

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 ${\pi }^{2}h=\pi (x{)}^2\times$ 2h

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

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

Hence the correct answer is (b) $\frac{1}{\sqrt{2}}$