What is the volume of the space inside the 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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Find the volume of the globe, which is a sphere. V = (4/3)πr³
Find the volume of the box. V = s³ {one side cubed}
Subtract the volume of the globe from the volume of the box.

Volume of the globe
V = (4/3)πr³
= (4/3)(3.14)(6³) {since the diameter is 12, the radius is 6}
= (4/3)(3.14)(216) {evaluated the exponent}
​≈ 904.32 {multiplied}

Volume of box
V = s³ {one side cubed}
= 12³ {substituted 12 in for s}
= 1728 {evaluated exponent}

Volume of space inside box not taken up by globe
= 1728 - 904.32 {subtracted volume of sphere from volume of box}
= 823.68 in³ {subtracted}

Ask Algebra House
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