SOLUTION: A sample of an alloy is in the shape of a solid sphere with a radius of 6.4cm. If this sphere is melted down and then cast into a cube, what is the length of an edge of the cube?

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Question 363515: A sample of an alloy is in the shape of a solid sphere with a radius of 6.4cm. If this sphere is melted down and then cast into a cube, what is the length of an edge of the cube?
Found 2 solutions by Fombitz, checkley77:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of a sphere is,
V%5Bs%5D=%284%2F3%29pi%2AR%5E3
The volume of a cube is,
V%5Bc%5D=s%5E3
The two volumes are equal.
s%5E3=%284%2F3%29pi%2AR%5E3
s=R%2Aroot%283%2C%284%2F3%29pi%29
highlight%28s=6.4%2Aroot%283%2C%284%2F3%29pi%29%29 or approximately,
s=10.3cm

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
V=(4/3)PIR^3
V=4/3*3.14*6.4^3
V=4.187*262.144
V=1,097.5 ANS FOR THE VOLUME OF THE SPHERE.
V=S^3 FOR THE CUBE.
1,1097.5=S^3
S=CUBERT1,097.6
S=10.315 cm. is the ans. for the length of the sides of the cube with a volume of 1,097.5.