Question

The ratio of curved surface area of two cylinders having the same height is 5:6. The ratio of their volumes will be equal to

• A. 5 : 6
• B. 5 : 36
• C. 25 : 6
• D. 25 : 36

Answer 1

The correct option is D

25 : 36

Let $r_1$ and $h_1$be the radius and height of cylinder 1

Let $r_2$ and $h_2$be the radius and height of cylinder 2

$\frac{\text{Curved Surface area 1}}{\text{Curved surface area 2}}=\frac{2\pi r_1{h}_1}{2\pi r_2{h}_2}$

$\Rightarrow \frac{5}{6}=\frac{r_{1}h}{r_{2}h}$

$\Rightarrow \frac{5}{6}=\frac{r_1}{r_2}$ (as h_1 = h_2)

Ratio of volume will be equal to

$\frac{V_1}{V_2}=\frac{\pi r_1^2{h}_1}{\pi r_2^2{h}_2}$

Since h_1 = h_2

$\frac{V_1}{V_2}=(\frac{r_1}{r_2}{)}^2=(\frac{5}{6}{)}^2=\frac{25}{36}=25:36$