Question

a cylinder and s come have equal heights and equal radius of their bases if their curved surface areas are in the ratio 8:5 then show that ratio of radius to height of each is 3:4​

Answer 1

Let the radius and height of cylinder and cone be r and h.

Let the slant height of cone be l.

CSA of cylinder : 2πrh

CSA of cone : πrl

Ratio = CSA of cylinder/CSA of cone = 2πrh/πrl = 8/5

⇒ h/l = 4/5

⇒ h²/l² = 16/25

⇒l² = (25/16)h²

⇒ h² + r² = (25/16)h²

⇒ r² = (9/16)h²

⇒ (r/h)² = (3/4)²

⇒ r/h = 3/4

hence ratio of radius to height is 3:4

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