Question
Download Solution PDFThe volume of a right circular cone, with a base radius the same as its altitude, and the volume of hemisphere are equal. The ratio of the radii of the cone to the hemisphere is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven that the radius of the cone = the height of the cone
Let the radius of cone be r and the radius of the hemisphere be R.
Given that the volume of the cone is equal to the volume of the hemisphere
⇒ 1/3πr2.r = 2/3πR3
⇒ r3 = 2R3
⇒ r3 = 2R3
∴ r ∶ R = ∛2 ∶ 1Last updated on Jun 11, 2025
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