Chapter 13, Problem 32PE

(a)

To determine

To show: The equation $\frac{y_0}{6380}=\frac{6380}{\left(6380+437\right)}$ holds by using similar triangles in the given figure and solve for $y_0$.

The value of distance $y_0$ is $\underset{\_}{5971\text{ km}}$.

(b)

To determine

The visible area by evaluating the integral $VA={\displaystyle \underset{y_0}{\overset{6380}{\int }}2\pi x\sqrt{1+{\left(\frac{dx}{dy}\right)}^2}}dy$.

(c)

To determine

To express: The visible area as a percentage of Earth’s surface area.