SOLUTION: A cube and a sphere each encloses 1000cm cubed. Which shape is taller, and by how much?

Question 1160561: A cube and a sphere each encloses 1000cm cubed. Which shape is taller, and by how much?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the volume of each is 1000 cubic centimeters.
the formula for the volume of a cube is s^3 = 1000.
s is the length of an edge of the cube.
this makes s = cube root of 1000 = 10 centimeters.
the formula for the volume of a sphere is 4/3 * pi * r^3 = 1000
solve for r to get r = (1000 / (4/3 * pi))^( 1/3) = 6.203504909 centimeters.
the diameter is equal to 2 times that = 12.40700982 centimeters.
the height of the sphere is the diameter of the sphere, therefore the sphere is taller, assuming the cube is laying on one of its sides.
the sphere is taller by 12.40700982 minus 10 = 2.40700982 feet.

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