The volume of a sphere is 4/3 x pi x r3
Half of that is 2/3 x pi x r3
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Volume of half a sphere = 2/3*pi*radius3 Volume = 2/38pi*103 = 2094.395102 cubic units
Volume of half sphere: (4/3*pi*15^3)/2 = 2250*pi cubic units
Volume of a sphere = 4/3*pi*radius3
Volume of a sphere = 4/3*pi*radius3 measured in cubic units
To determine empty space, we will assume that the sphere fits snugly(so that each side of the cube is touching the sphere). First, we take the volume of the cube, which is just one of its side lengths cubed(side length X side length X side length). Record this quantity. Then we find the volume of the sphere. The formula for the volume of a shere is (4/3) Pi r cubed. Since the sphere fits snugly, we know that the radius is half of the side length. We then take the cube volume and subtract the sphere volume, and that is the empty space remaining.