SOLUTION: I have been working on this math problem and i can't seem to figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it! Sphere

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Question 305002: I have been working on this math problem and i can't seem to figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!
Spheres
Four solid metal balls fit snugly inside a cylindrical can. A geometry student claims that two extra balls of the same size can be put into the can, provided all six balls can be melted and the molten liquid poured into the can. Is the student correct? (hint: let the radius of each ball be r.)
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Four solid metal balls fit snugly inside a cylindrical can.
A geometry student claims that two extra balls of the same size can be put into the can, provided all six balls can be melted and the molten liquid poured into the can.
Is the student correct? (hint: let the radius of each ball be r.)
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Volume of the can:
Vc = (pi)r^2*h
Note: h = 8r
Vc = (pi)r^2*(8r)
Vc = (8pi)r^3
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Volume of the 4 balls:
4Vb = 4(4/3)(pi)r^3
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Volume remaining when only 4 balls are in the can:
(8pi)r^3 - (16/3)(pi)r^3
= (8-(16)3))(pi)r^3
= (8/3)(pi)r^3
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Can volume of 2 balls fit into that remaining space?
[(8/3)(pi)r^3]/[(4/3)(pi)r^3] = 2
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Answer: Yes
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Cheers,
Stan H.
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