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 cubic inch, of the space inside the box that is not taken up by the globe

823.68 is the amount of space not taken up by the globe.

Step-by-step explanation:

Formulas

d = 2*r

r = d/2 = 12/2 = 6

The volume of the shipping box is V = s^3

The volume of the globe is V = (4/3) * pi * r^3

Solution

V_cube = 12^3 = 1728

V_globe = (4/3) * 3.14 * 6^3

V_globe = 4.18 * 6^3

V_globe = 4.18 * 216

V_globe = 904.32

The unoccupied space = V_cube - V_globe

The unoccupied space = 1728 - 904.32 = 823.68