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?

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}

4

--- πr³

**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}

V = s³

**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__