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A sphere, a cylinder and a cone have the same diameter. The height of the cylinder and also the cone are equal to the diameter of the sphere. The ratio of their volumes is

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1 : 2 : 3

4 : 2 : 3

2 : 3 : 1

5 : 4 : 2

answer is C.

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Detailed Solution

It is given that, diameter of the sphere, cylinder and cone is the same.
So, the radius will also be the same i.e., r.
Also, given that, height of the cylinder =diameter of sphere= 2r.
And height of the cone = 2r.
We know that,
Volume of sphere=

43 π r 3

.
Volume of cone=

13 π r 2 h

So, according to question volume of cone=

13 π r 2 (2 r)

.
Volume of cylinder=

π r 2 h

.
So, according to question volume of cylinder=

π r 2 (2 r)

.
Thus, the ratio of their volumes is,
Volume of sphere : Volume of cone : Volume of cylinder

⇒ 43 π r 3 : 13 π r 2 (2 r) : π r 2 (2 r)

⇒

43 π r 3 : 23 π r 3 : 2 π r 3

⇒ 43 : 2 : 23 ⇒ 4 : 6 : 2 ⇒ 2 : 3 : 1

Therefore, the correct option is 3.

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