Chapter 0.7, Problem 16E

To determine

To calculate: The length of tunnel that could be dug to the center of the Earth whose circumference of equator is about $\text{2500 miles}$ .

Answer to Problem 16E

The length of tunnel that could be dug from the surface of Earth’s equator to the center of it is $\text{397}\text{.7 miles}$ .

Explanation of Solution

Given information:

The circumference of Earth’s equator is approximately $\text{2500 miles}$ .

Formula used:

Circumference $\left(C\right)$ of a circle with radiusr is given by $C=2\pi r$ .

A straight line from surface to center of circle represents the radius of the circle.

Calculation:

Consider the given statement that the circumference of Earth’s equator is approximately $\text{2500 miles}$ .

Recall that a straight line from surface to center of circle represents the radius of the circle.

So, the length of tunnel that could be dug from the surface of Earth’s equator to the center will represent the radius of it.

Recall that the circumference $\left(C\right)$ of a circle with radius r is given by $C=2\pi r$ .

Apply it,

  $\begin{array}{c}C=2\pi r\\ 2500=2\cdot \frac{22}{7}\cdot r\\ \frac{2500\times 7}{2\times 22}=r\\ 397.72\approx r\end{array}$

Rounding off to the nearest tenth, we get,

  $r=\text{397}\text{.7 miles}$

Thus, the length of tunnel that could be dug from the surface of Earth’s equator to the center of it is $\text{397}\text{.7 miles}$ .