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7 October, 15:45

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

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  1. 7 October, 15:47
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    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.
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