Chapter 12.6, Problem 44PPS

a.

To determine

Explain the longest latitude line and the geometric name for the circle that will created.

Answer to Problem 44PPS

The longest latitude is equator and the name of the circle is great circle.

Explanation of Solution

Given:

It is given in the question that the latitude lines circle Earth in an east west direction.

Since, from the given statement, the longest latitude line is the equator, A diameter of the circle is a diameter of the sphere . This is known as a great circle.

b.

To determine

Calculate the surface area of the earth.

Answer to Problem 44PPS

The surface area of the earth is $199,045,414.1mile{s}^2$ .

Explanation of Solution

Given:

It is given in the question that the circumference of the earth is about $25,000$ miles.

Concept Used:

In this, use the concept of surface area of the sphere and know the formula of circumference i.e. $S=4\pi r^2$ & $C=2\pi r$ .

Calculation: Here, $C=25,000$

  $\begin{array}{l}C=2\pi r\\ 25000=2\pi r\\ r=\frac{25000}{2\pi }\\ r=\frac{25000}{6.28}\\ r=3980.9miles\end{array}$

Now, the surface area is $S=4\pi r^2=4\pi {(3980.9)}^2=63390259.2\pi =199,045,414.1mile{s}^2$

Conclusion:

The surface area is $199,045,414.1mile{s}^2$ .

c.

To determine

Explain the property that can applied to latitude lines.

Answer to Problem 44PPS

The latitudes have the same degree for the congruent circles.

Explanation of Solution

Given:

It is given in the question that there will be two planes which are equidistant from the center of a sphere and intersect the sphere then the circles of intersection are congruent.

Since, if the two planes are equidistant from the center and intersect it , then it will be congruent because the latitudes have the same degree that will be congruent circles. For example ( ${30}^{\circ }N$ & ${30}^{\circ }S$ ).