SOLUTION: A jeweler has three small solid spheres made of gold, of radius 2mm, 3mm, and 4mm. He decides to melt these down and make just one sphere out of them. What will the radius of this

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Question 31263This question is from textbook College Algebra
: A jeweler has three small solid spheres made of gold, of radius 2mm, 3mm, and 4mm. He decides to melt these down and make just one sphere out of them. What will the radius of this larger sphere be?
Thank you so very much!This question is from textbook College Algebra

Answer by mbarugel(146) About Me  (Show Source):
You can put this solution on YOUR website!
Hello!
We need to use the formula for the volume of a sphere:
V+=+%284%2F3%29pi%2Ar%5E3
where r is the radius.
The jeweler has 3 spheres of gold. Let's see the total volume of gold he has:
%284%2F3%29pi%2A2%5E3+%2B+%284%2F3%29pi%2A3%5E3+%2B+%284%2F3%29pi%2A4%5E3+=+414.69023
He 414.69023... cubic mm of gold. Therefore, when he makes one sphere, its volume will be exactly that value. Now, using the volume formula, we can find the radius of a shpere that has that volume:
414.69023+=+%284%2F3%29pi%2Ar%5E3
132+=+%284%2F3%29r%5E3
99+=+r%5E3
r+=+99%5E%281%2F3%29=4.62606
So the new sphere will have a radius of 4.62606... mm

I hope this helps!
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