Question

Two cylindrical pots contains the same amount of water. If their diameters are in the ratio $2:3$, then what is the ratio of their heights ?

• A. $\frac{9}{4}$
• B. $\frac{7}{4}$
• C. $\frac{9}{5}$
• D. $\frac{8}{5}$

Answer 1

The correct option is A $\frac{9}{4}$

Let the diameters of the pots be $d_1=2x$ and $d_2=3x$, respectively.

Let $r_1,h_1$ and $r_2,h_2$ be the radii and height of the two cylinders, respectively.

Then, $\pi r{{}_1}^2{h}_1=\pi r{{}_2}^2{h}_2$

$\Rightarrow \frac{h_1}{h_2}=\frac{r{{}_2}^2}{r{{}_1}^2}$

$\Rightarrow {\left(\frac{r_2}{r_1}\right)}^2={\left(\frac{d_2/2}{d_1/2}\right)}^2={\left(\frac{3x/2}{2x/2}\right)}^2=\frac{9}{4}$