Question 31263
Hello!
We need to use the formula for the volume of a sphere:

{{{V = (4/3)pi*r^3}}}
where r is the radius.

The jeweler has 3 spheres of gold. Let's see the total volume of gold he has:

{{{(4/3)pi*2^3 + (4/3)pi*3^3 + (4/3)pi*4^3 = 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 = (4/3)pi*r^3}}}
{{{132 = (4/3)r^3}}}
{{{99 = r^3}}}
{{{r = 99^(1/3)=4.62606}}}

So the new sphere will have a radius of 4.62606... mm


I hope this helps!
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