Question

A couple of two way radios were purchased from different stores. Two way radio A can reach 8 miles in any direction. Two way radio B can reach 11.27 kilometers in any direction.

Part A: How many square miles does two way radio A cover? Use 3.14 for TT and round to the nearest whole number.

B. Part A: How many square miles does two way radio B cover? Use 3.14 for TT and round to the nearest whole number.

C. If 1 mile= 1.61 kilometers, which two way radio covers the larger area?

D. Using the radius of each circle, determine the scale factor relationship between the radio coverages.

Answer 1

Explanation:

A) To find the area covered by two-way radio A, we need to calculate the area of a circle with a radius of 8 miles:

Area = πr² = 3.14 x 8² = 200.96 square miles

Rounding to the nearest whole number, two-way radio A covers 201 square miles.

B) To find the area covered by two-way radio B, we need to convert the radius from kilometers to miles and then calculate the area of a circle with that radius:

Radius in miles = 11.27 / 1.61 = 6.9988 miles (rounded to 4 decimal places)

Area = πr² = 3.14 x (6.9988)² = 153.94 square miles

Rounding to the nearest whole number, two-way radio B covers 154 square miles.

C) Two-way radio A covers a larger area than two-way radio B (201 square miles vs 154 square miles).

D) The scale factor relationship between the radio coverages can be found by dividing the radius of radio A by the radius of radio B:

Scale factor = radius of A / radius of B = 8 miles / (11.27 km / 1.61 km/mile) = 4.97

This means that the coverage of two-way radio A is almost 5 times larger than that of two-way radio B.