A solid is in the shape of a cone mounted on a hemisphere of same base radius. If the curved surface areas of the hemispherical part and the conical part are equal, then find the ratio of the radius and the height of the conical part.

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32

13

23

12

answer is B.

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Detailed Solution

Given that, curved surface area of hemisphere is equal to conical part.
The curved surface area of the cone is

π r l

and hemisphere is

2 π r 2

where r is radius and l is slant height.
Here,

⇒ π r l = 2 π r 2 ⇒ r 2 + h 2 = 2 r ⇒ r 2 + h 2 = 4 r 2 ⇒ 3 r 2 = h 2

Therefore,

⇒ r 2 h 2 = 13 ⇒ r h = 13

Thus, the ratio of the radius and height of the conical part is

13

.
Therefore, option (2) is correct.

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