A sphere having a radius R is melted and recast into a hemisphere and a cylinder. The hemisphere and cylinder have equal radii and heights. If the height of the cylinder is equal to its radius r, find the ratio R:r.
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Correct answer: A
Explanation
Volume of sphere = (4/3)πR³
Volume of hemisphere = (2/3)πr³
Radius of cylinder = r, height = r
Volume of cylinder = πr² × r = πr³
Total new volume = (2/3)πr³ + πr³ = (5/3)πr³
(4/3)πR³ = (5/3)πr³
4R³ = 5r³
R³/r³ = 5/4
R/r = ∛(5/4)
R : r = ³√5 : ³√4