Q11 of 56 Page 13

A solid is hemispherical at the bottom and conical (of same radius) above it. If the surface areas of the two parts are equal then the ratio of its radius and the slant the height of the conical part is (CBSE 2012)

Given: Bottom of a solid is hemispherical and conical above it, both have same radius


and same surface areas.


∴ CSA of hemisphere = CSA of Cone


⇒ 2 × π × r2 = πrl (where r is the radius and l is the slant height)


⇒ =


⇒ =


∴ r:l = 1:2


That is ratio of radius and the slant height of the given solid is 1:2.

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