A solid hemisphere is melted into a smaller hemisphere and a sphere of equal radii. If the smaller hemisphere’s radius is r, find the radius R of the original hemisphere.
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Correct answer: A
Explanation
Volume of the original hemisphere = Volume of the new hemisphere + Volume of the new sphere
(2/3)πR³ = (2/3)πr³ + (4/3)πr³
(2/3)πR³ = 2πr³
R³ = 3r³
R = ∛3 × r