A sphere with this volume has a diameter of 9.1416 cm, a surface area of 262.54 square cm and a circumference of 28.719 cm.
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volume is 4/3 pi x the redius cubed
3 grams per cubic centimeter :D
I'm quite sure this is impossible to prove, because the volume of a sphere is not equal to the volume of a cylinder with the same radius and height equal to the sphere's diameter. This can be shown as: Volume of sphere = (4*pi*r3) / 3. Volume of cylinder = pi*r2*h. Here, the height, h, of the cylinder = d = 2r. So, the volume of the cylinder = pi*r2*2r = 2*pi*r3, which obviously does not equal the volume of the sphere. The volume of half a sphere (with radius r) is equal to the volume of a cylinder(whose height is equal to its radius, r) minus the volume of a cone with the same height and radius. Therefore, the volume of a sphere is just double that. If you follow the nearby link, you can see a nice demonstration of that.
Volume = e3 where e is the edge length. So, 83 = 512 cubic cm
Volume of cube: 10*10*10 = 1000 cubic m