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A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.

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4 : 1

2 : 5

2 : 3

2 : 1

answer is D.

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Detailed Solution

It is given a cone and a hemisphere.
Let the radius be

r

.
Let the height of the cone be

h

.
Given, the height of the hemisphere is equal to its radius.
The volume of the cone and hemisphere is equal.
We know, volume of cone is,

V = 13 π r 2 h

.
Volume of a hemisphere of radius

V = 23 π r 3

.
As both the volumes are equal,

13 × π × r 2 × h = 23 × π × r 3

h = 2 r

h r = 21

Hence, the required ratio is

2 : 1

.
Therefore, the correct option is 4.

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