A solid hemisphere is drilled with a cylindrical with radius R hole through its center. If the height of the removed cylinder equals the hemisphere’s radius R, find the ratio of the volume removed to the volume remaining.
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Correct answer: D
Explanation
Volume of the hemisphere = 2/3 πR³
Volume of the cylinder (r = R/2, h = R) = π × (R/2)² × R = 1/4 πR³
Remaining volume = 2/3 πR³ − 1/4 πR³ = 5/12 πR³
Ratio (removed : remaining) = 1/4 : 5/12 = 3 : 5