A sports company wants to package a ball with a 1.5-inch radius in sets of two. They have two options: a cylinder or a square prism. The company wants to use the package that has the least amount of wasted space. The company should choose

The answer is a cylinder.

A cylinder will eate the least amount of space.

Space is measured by volume.

You can calculate the volume of the two balls as the volumes of two identical spheres:

2 balls * [4/3 * π * (r^3) inch^3 / ball = 2 * 4/3 * π * (1.5inch) ^3 = 28.27 inch^3.

The volume of a cylindrical package to contain the two balls would be:

area of the base * height

[π * r^2 ] * [2 * diameter of the balls ] = π * (1.5 inch) ^2 * [2 * 2 * 1.5 inch] = 42.4 inch^3

The volume of a pyramidal package to contain the two balls would be:

area of the base * height

[ (2 * 1.5 inch) ^2] * [2 * 2 * 1.5 inch ] = 54 inch^3

There you see that the wasted space using the package in form of square pyramid is greater than when using a package in form of cylinder.