Chapter 7.7, Problem 65PPS

To determine

To Find:

Radius of the region.

Answer to Problem 65PPS

About 282 feet.

Explanation of Solution

Given Information:

The organizers of a concert are preparing for the arrival of 50,000 people in the open field where the concert will take place. Each person is allotted 5 square feet of space, so the organizers rope off a circular area of 250,000 square feet. Using the formula $A=\pi r^2$ , where A represents the area of the circular region and r represents the radius of the region.

Calculation:

  $\begin{array}{l}Given\\ A=250000\\ \text{Substituting the value of 'A' in the equation of area and solving it to }\\ \text{find the radius of the region:}\\ A=\pi r^2\\ \Rightarrow 250000=\pi r^2\\ \Rightarrow r^2=\frac{250000}{\pi }\mathrm{.............}[\text{divide each side by }\pi \text{]}\\ \Rightarrow r=\sqrt{\frac{250000}{\pi }}=\frac{500}{\sqrt{\pi }}\approx 282\end{array}$

So, the radius of the region is about 282 feet.