Question

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?
cubic inches

Explanation:

Step1: Calculate the volume of the cube

The volume formula of a cube is \(V = s^3\), where \(s\) is the side - length. Given \(s = 12\) inches, then \(V_{cube}=12^3=12\times12\times12 = 1728\) cubic inches.

Step2: Calculate the volume of the globe (sphere)

The volume formula of a sphere is \(V=\frac{4}{3}\pi r^3\). Given the diameter \(d = 12\) inches, the radius \(r=\frac{d}{2}=6\) inches. Substitute \(r = 6\) into the formula: \(V_{sphere}=\frac{4}{3}\pi(6)^3=\frac{4}{3}\pi\times216 = 288\pi\approx288\times3.14 = 904.32\) cubic inches.

Step3: Calculate the unoccupied volume

Subtract the volume of the sphere from the volume of the cube. \(V = V_{cube}-V_{sphere}\). So \(V=1728 - 904.32=823.68\) cubic inches.

Answer:

\(823.68\)