Math 182 Miniproject 4 The Volume of a Football.md
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Math 182 Miniproject 4 The Volume of a Football
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**Overview:** In this project we find exact formulas for integral approximations using Riemann sums of various flavors.

**Prerequisites:** Section 6.2 of _Active Calculus_.

Go to https://www.desmos.com/calculator/c7aip1g33m to see a regulation size football image. (All units are inches.)

1. Using your graph plotting kung fu, find a curve that approximates the boundary of (at least part of) the football.

$f\left(x\right)=1.6\sqrt{x+5.5}$

2. Set up an integral expression that will give the volume of the football.

$A=\pi\left(1.6\sqrt{x+5.5}\right)^{2}$
$V=2\int_{-5.5}^{0}\left(\pi\left(1.6\sqrt{x+5.5}\right)^{2}\right)dx$

3. Use Desmos to find the value of your integral. What is the volume of the football?

$V=2\int_{-5.5}^{0}\left(\pi\left(1.6\sqrt{x+5.5}\right)^{2}\right)dx$
$V=243.284935094$

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