Chapter 6, Problem 18RE

To determine

To estimate: the volume of a football.

Answer to Problem 18RE

  $Volume\approx 1290c{m}^3$

Explanation of Solution

Given information: The football is 28 cm long and circumference at its widest point to

be 53 cm, the circumference 7 cm from each end is 45 cm.

Calculation:

From the given data, there will be n =4 intervals. Intervals width:

  $△x=\frac{b-a}{n}=\frac{28-0}{4}=7.$

They give the circumference, so the radius will be $r=\frac{circumference}{2\pi }$ .

Fill in the radius values from the given circumferences at increments of $△x$ .

x	r
0	0
7	$\frac{45}{2\pi }$
14	$\frac{53}{2\pi }$
21	$\frac{45}{2\pi }$
28	0

Therefore,

  $\begin{array}{l}$ V=2\pi {\displaystyle \underset{0}{\overset{28}{\int }}{r}^2}dx\approx \frac{△x}{3}[f{(x_0)}^2+4f{(x_1)}^2+2f{(x_2)}^2+4f{(x_3)}^2+f{(x_4)}^2]$$ V\approx \frac{7}{3}[0+4{(\frac{45}{2\pi })}^2+2{(\frac{53}{2\pi })}^2+4{(\frac{45}{2\pi })}^2+0]$V\approx 1290c{m}^3\end{array}$