Question

two cylinders have same lateral surface area.their radii are in the ratio 3:2 . find the ratio of their heights.

Answer 1

ratio of their heights = 2:3

Answer 2

Answer:

$\text{Ratio of their heights is }2:3$

Step-by-step explanation:

Given that two cylinders have same lateral surface area and their radii are in the ratio 3:2 .

we have to find the ratio of their heights.

$\text{Let }r_1\text{ and }h_1\text{ are radius and height of one cylinder and }$

$r_2\text{ and }h_2\text{ are radius and height of second cylinder }$

Also, $r_1:r_2=3:2$

Lateral surface area of cylinder=2πrh

Given the two cylinder with same lateral surface area

$2\pi r_1 h_1=2\pi r_2 h_2$

⇒ $\frac{h_2}{h_1}=\frac{r_1}{r_2}=\frac{3}{2}$

$Hence, \text{Ratio of their heights is }2:3$