A cylinder and a cone have equal base radii and equal heights . if their c.s.a. are in ratio 8:5, what is the ratio of their radii to heights ?
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Step-by-step explanation:
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
⇒\boxed{r/h = 3/4}
hence ratio of radius to height is 3:4.
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