A cone, a hemisphere and a cylinder are formed on the same base and with the same height. The ratio of their volumes is:

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2: 1: 3

1: 2: 3

3: 1: 2

1: 3: 2.

answer is B.

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Detailed Solution

It is given that a cone, a hemisphere and a cylinder are formed on the same base and with same height.
Volume of Hemisphere =

23 π r 3

Volume of cone =

13 π r 2 h

Volume of Cylinder =

π r 2 h

Now, the ratio of their volumes is given by,

⇒ (13) π r 2 h : (23) π r 3 : π r 2 h

Here, h = r.

⇒ (13) π r 2 r : (23) π r 3 : π r 2 r

⇒ (13) π r 3 : (23) π r 3 : π r 3

⇒ 13 : 23 : 1

⇒ 1 : 2 : 3

So, the ratio of the volumes

= 1 : 2 : 3

.
Hence, the correct option is 2.

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