A cylinder and a cone have equal radii of their bases and equal height

1.	A cylinder and a cone have equal radii of their bases and equal heights.If their curved surface areas are in the ratio 8:5, show that the radiusand height of each has the ratio 3:4.
Answer» Let the radius and height of cylinder and cone be r and h.Let the slant height of cone be l. CSA of cylinder : 2πrhCSA 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

A cylinder and a cone have equal radii of their bases and equal heights.If their curved surface areas are in the ratio 8:5, show that the radiusand height of each has the ratio 3:4.

Answer»

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

CSA of cylinder : 2πrhCSA 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