Chapter 8, Problem 23RE

To determine

To find : the volume of the football to the nearest cubic inch.

Answer to Problem 23RE

The volume of the football is $88\pi$ .

Explanation of Solution

Given information : the profile of a football resembles the ellipse shown here:

  

Calculation :

The volume generated by revolving the figure about the x -axis:

  $\begin{array}{l}{\displaystyle \underset{\raisebox{1ex}{$-11$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{\overset{\raisebox{1ex}{$11$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{\int }}\pi \left(12\right)\cdot \left(1-\frac{4x^2}{121}\right)}dx\\ \Rightarrow 12\pi x-\frac{16\pi x^3}{121}\\ \Rightarrow 12\pi \left(x-\frac{4x^3}{363}\right)\\ \Rightarrow 88\pi \end{array}$