Question

If the volume of cylinder is $12436c{m}^3$ and radius and height of cylinder are in the ratio $2:3$, find its height.

• A. $21cm$
• B. $7cm$
• C. $14cm$
• D. $18cm$

Answer 1

The correct option is A $21cm$

We have,

The volume of cylinder$=12436c{m}^3$

Let the height $=h$

Radius $=r$

Now,

$\frac{r}{h}=\frac{2}{3}$

$3r=2h$

$\Rightarrow r=\frac{2h}{3}$

Now,

$\text{Volume}\text{of}\text{cylinder}=12436$

$\pi r^{2}h=12436$

${\left(\frac{2h}{3}\right)}^{2}h=\frac{12436\times 7}{22}$

$\frac{4h^3}{9}=\frac{12436\times 7}{22}$

$\Rightarrow h^3=\frac{12436\times 7\times 9}{22\times 4}$

$\Rightarrow h^3=8903.045$

$\Rightarrow h=20.72\approx 21cm.$

Hence, this is the answer.