Volume with globe in a box

A globe has a diameter of 12 inches.  It fits inside a cube-shaped box that has a side length of 12 inches.  What is
the volume, rounded to the nearest hundredth of a cubic inch, of the space inside the box that is not taken up by the globe?
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The volume of a globe (sphere) is:
4
--- πr³   {volume of a sphere}
3

The radius of the globe is 6.   {radius is half the diameter}

Volume of the globe
V = (4/3)(3.14)(6³)   {substituted 6 for r and 3.14 for π into volume formula}
≈  (4/3)(3.14)(216)   {evaluated exponent}
≈  904.32 in³   {multiplied}

The volume of a cube-shaped box:
V = s³   {one side, cubed}

Volume of the box
V = 12³   {substituted 12, in for s, into volume formula}
=  1728 in³   {evaluated exponent}

The space inside the box not taken up by the globe
≈  1728 - 904.32   {volume of box minus volume of globe}
≈  823.68 in³   {subtracted}

Ask Algebra House
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