# Algebra 1

Mrs. Isabelle is making paper and plastic foam animals for her first-grade class. She is calculating the amount of wasted materials for environmental and financial reasons.

Mrs. Isabelle's class is making plastic foam spheres out of plastic foam cubes. Enter the polynomial that represents the amount of plastic foam wasted if the class cuts out the biggest spheres possible from cubes with side lengths of l. The volume of a sphere of radius r is
4/3πr^3.

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1. L = 2 r
volume sphere = (4/3) pi r^3
volume cube = (2r)^3 = 8 r^3
waste = vol cube - vol sphere
= [ 8 - (4/3)pi ] r^3
= 3.81 r^3 approximately
fraction wasted = 3.81 / 8 = .48 or waste almost half

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👨‍🏫
Damon

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