A solid hemisphere is drilled with a cylindrical with radius R/2 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
Radius of the hemisphere = R
Radius of the cylindrical hole = R/2
Height of the removed cylinder = R
The removed part is considered to be only the cylinder.
Volume of the hemisphere = (2/3)πR³
Volume of the removed cylinder = πr²h
= π × (R/2)² × R
= (1/4)πR³
Remaining volume = (2/3 − 1/4)πR³
= (8 − 3)/12 πR³
= (5/12)πR³
= Removed : Remaining
= (1/4) : (5/12)
= 3 : 5