Item 18 A spherical ball with a volume of 972π in.3 is packaged in a box that is in the shape of a cube. The edge length of the box is equal to the diameter of the ball. What is the volume of the box?

check the picture below.

so, the diameter of the sphere, is the same as a side's length of the cube, bearing in mind that all sides in a cube are the same length.

since all sides in the cube are "d", then its volume is V = d*d*d or V = d³.

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ -----\\ V=972\pi \end{cases}\implies 972\pi =\cfrac{4\pi r^3}{3}\implies 2916\pi =4\pi r^3 \\\\\\ \cfrac{2916\pi }{4\pi }=r^3\implies 729=r^3\implies \sqrt[3]{729}=r\implies \boxed{9=r}[/tex]

since the diameter is twice as much as the radius, thus d = 2r, or namely d = 18.

therefore, the volume of the cube will be V = 18³.