A hemisphere has radius R. A sphere of maximum possible radius is inscribed in the hemisphere such that it touches the curved surface internally and rests on the hemisphere’s base. Find the ratio of their surface areas.
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Correct answer: A
Explanation
Radius of the hemisphere = R
Radius of the sphere = r
Distance from the center of the hemisphere to the center of the sphere = r
Due to internal contact—
R − r = r
R = 2r
r = R/2
Ratio—
3πR² : 4π(R/2)²
3πR² : πR²= 3 : 1