# The height of a circular cylinder of given volume varies inversely as the square of the radius of the base. How many times greater is the radius of a cylinder 3 m high than the radius of a cylinder 6 m high with the same volume?

Aug 27, 2017

The radius of cylinder of $3$ m high is $\sqrt{2}$ times greater
than that of
$6 m$ high cylinder.

#### Explanation:

Let ${h}_{1} = 3$ m be the height and ${r}_{1}$ be the radius of the 1st cylinder.

Let ${h}_{2} = 6$m be the height and ${r}_{2}$ be the radius of the 2nd cylinder.

Volume of the cylinders are same .

$h \propto \frac{1}{r} ^ 2 \therefore h = k \cdot \frac{1}{r} ^ 2 \mathmr{and} h \cdot {r}^{2} = k \therefore {h}_{1} \cdot {r}_{1}^{2} = {h}_{2} \cdot {r}_{2}^{2}$

$3 \cdot {r}_{1}^{2} = 6 \cdot {r}_{2}^{2} \mathmr{and} {\left({r}_{1} / {r}_{2}\right)}^{2} = 2 \mathmr{and} {r}_{1} / {r}_{2} = \sqrt{2}$ or

${r}_{1} = \sqrt{2} \cdot {r}_{2}$

The radius of cylinder of $3$ m high is $\sqrt{2}$ times greater

than that of $6 m$ high cylinder [Ans]