A globe has a diameter of 12 inches. It fits inside a cubeshaped 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?
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 cubeshaped 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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Geometry State Test Practice Archives
November 2019
