word problem geometry

Question

The listening area for a radio station extends 72 miles in every direction from its signal tower. What is the size of the stations listening area?

Answer 1

Since the listening area extended to 72 miles in every direction from its signal tower, it forms a circle with a center at the signal tower and a radius of 72 miles. Therefore,

Listening Area = Pi * R² = 3.14 * 72² = 16,277.76 square miles

(Set Pi = 3.14 to simplify the answer)

Answer 2

Area of a circle = pi * r^2

A = (3.14)(72^2)

A = 16278 miles^2

Answer 3

Think about what area of a circle is, and what the area is in the problem. Then solve!