Problema Solution
A jeweler has three small solid spheres made of gold, of radius 2mm, 3mm, and 4mm. He decided to melt these down and make just one sphere out of them. What will the radius of the larger sphere be?
Answer provided by our tutors
let
r = the radius of the larger sphere, r>0
the volume of the larger sphere = sum of the volumes of the smaller spheres
(4/3) r^3 pi = (4/3) 2^3 pi + (4/3) 3^3 pi + (4/3) 4^3 pi
divide both sides by (4/3)pi
r^3 = 2^3 + 3^3 + 4^3
by solving we find:
r^3 = 99
r = 4.63 mm
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the radius of the larger sphere will be 4.63 mm.