Question

11. If two cylinders of same lateral surface area have their radii in the ratio 4:9, then
the ratio of their heights is
​

Answer 1

Refer to the attachment!

Answer 2

Given,

Ratio of their radii = 4:9

They have same lateral surface area.

To find,

The ratio of their heights.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Let, their radii = 4x and 9x units

And, their heights = a and b units

Lateral surface area of first cylinder = (2×π×4x×a) = 8πax sq. units

Lateral surface area of second cylinder = (2×π×9x×b)= 18πbx sq. units

According to the data mentioned in the question,

8πax = 18πbx

8a = 18b

a/b = 18/8

a/b = 9/4

a : b = 9 : 4

Hence, the height of their ratio is 9:4