Question

A right circular cylinder and a cone have equal bases and equal heights. If their

curved surface areas are in the ratio 8: 5, show that the ratio between radius of their

bases to their height is 3: 4.​

Answer 1

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Answer 2

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