The radius of a sphere and a right circular cylinder are equal and their curved surface areas are also equal. The ratio of their volumes is?

Q: The radius of a sphere and a right circular cylinder are equal and their curved surface areas are also equal. The ratio of their volumes is?

Given, 4πr2 = 2πrh ∴ h = 2r Now, required ratio = 4/3πr3 : πr2h = 4r : 3h = 4r : 6r [ ∴ h = 2r] = 2 : 3

3 : 4
2 : 3
3 : 2
4 : 3

Correct Answer: 2 : 3

Explanation:

Given, 4πr² = 2πrh
∴ h = 2r
Now, required ratio
= 4/3πr³ : πr²h
= 4r : 3h
= 4r : 6r [ ∴ h = 2r]
= 2 : 3

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