Question

Four 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 down and the molten liquid poured into the can. Is the student cottect? Let the radious of balls be r.

Answer 1

The volume of the metal in 6 balls is
6*(4/3)*pi*R^3 = 8 pi R^3

The cylinder has radius R and height 8R. Its volume is
pi*R^2*L = 8 pi R^3

They are exactly the same, so the metal from six molten balls will fit inside the can.