Question

#: If radii of two circular cylinders are in ratio of 3:2
and their heights are in the ratio of 8:9, find the
ratio of their lateral surface areas.​

Answer 1

Step-by-step explanation:

Let the radii of the two cylinders be r1 and r2 respectively and let the heights be h 1 and h 2 respectively .

⇒ The lateral surfaces of the two cylinders are 2πr1h1 and 2πr2h2 respectively.

⇒ The ratio of the lateral surfaces of the two cylinders is 2πr1h12πr2h2=r1h1r2h2.

It is given that the radii are in the ratio 3:2 and the heights are in the ratio 8:9.

⇒r1r2=32 and h1h2=89.

⇒r1h1r2h2=(32)(89)=43.

⇒ The ratio of the lateral surfaces of the two cylinders is 43.