Question

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?

Answer 1

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.

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

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.