SOLUTION: A wooden cube with a volume of 45cm3 is carved into the largest sphere and cylinder possible. Determine the volume of the wood which must be carved off and also the percentage redu

Algebra ->  Volume -> SOLUTION: A wooden cube with a volume of 45cm3 is carved into the largest sphere and cylinder possible. Determine the volume of the wood which must be carved off and also the percentage redu      Log On


   

Question 1071229: A wooden cube with a volume of 45cm3 is carved into the largest sphere and cylinder possible. Determine the volume of the wood which must be carved off and also the percentage reduction in the surface area(ignoring the wood shavings).
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let the diameter of the sphere equal one side of the cube.
Then the volume will be,
V%5Bs%5D=%284%2F3%29pi%28S%2F2%29%5E3=%28pi%2F6%29S%5E3
Originally the cube volume was,
V%5Bc%5D=S%5E3
So the difference is,
V%5Bc%5D-V%5Bs%5D=S%5E3-%28pi%2F6%29S%5E3
V%5Bc%5D-V%5Bs%5D=%286%2F6-pi%2F6%29S%5E3
V%5Bc%5D-V%5Bs%5D=%28%286-pi%29%2F6%29S%5E3
Substituting,
V%5Bc%5D-V%5Bs%5D=%28%286-pi%29%2F6%2945
V%5Bc%5D-V%5Bs%5D=%2815%2F2%29%286-pi%29cm%5E3