Chapter 12.7, Problem 19PPS

To determine

Find the distance between the point J and K on the sphere.

Answer to Problem 19PPS

The distance between the point J and K is $14.0in$ .

Explanation of Solution

Given:

It is given in the question that the figure is given below and $m\stackrel{⌢}{JK}=100$ :

  

Concept Used:

In this, use the concept of circumference of the circle i.e. $C=2\pi r$ .

Calculation:

Here, $r=8in$ , use the circumference formula,

  $\begin{array}{l}C=2\pi r\\ C=2\pi (8)\\ C=16\pi \\ C=50.26(\pi =3.14)\end{array}$

Now, it is also given that the measure of arc JK is $100$ degrees. So find out in the fraction : $\frac{100}{360}=\frac{5}{18}$ .

Now, it has to find out the $\frac{5}{18}$ of the circumference to get distance: $\frac{5}{18}\times 50.62=13.9625\approx 14.0$

Conclusion:

The distance is $14.0in$ .