Question

Quickly

A couple of two-way radios were purchased from different stores. Two-way radio A can reach 5 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 it and round to the nearest whole number. Show every step of your work. (3 points)
Part B: How many square kilometers does two-way radio B cover? Use 3.14 for π and round to the nearest whole nubber. Show every step of your work.
Part C: If 1 mile = 1.61 kilometers, which two-way radio covers the larger area? Show every step of your work.
Part D: Using the radius of each circle, determine the scale factor relationship between the radio coverages.

Answer 1

Part A:
The area of a circle is given by the formula A = πr^2, where A is the area, π is approximately 3.14, and r is the radius of the circle. For two-way radio A, r = 5 miles. Therefore, the area covered by two-way radio A is:
A = πr^2 = 3.14 × 5^2 = 78.5 square miles.

Part B:
To convert kilometers to miles, we multiply by 0.62137. Therefore, the range of two-way radio B in miles is:
11.27 km × 0.62137 mi/km = 7.00 miles
The area covered by two-way radio B is:
A = πr^2 = 3.14 × 7^2 = 153.86 square miles.

Part C:
To compare the areas covered by two-way radio A and two-way radio B, we need to convert the area of two-way radio B from square miles to square kilometers.
The area covered by two-way radio B is:
A = πr^2 = 3.14 × (11.27/1.61)^2 = 78.5 square kilometers.
Therefore, two-way radio B covers a larger area than two-way radio A.

Part D:
The radius of two-way radio A is 5 miles, and the radius of two-way radio B is 11.27 kilometers. To compare the areas covered by the two radios, we need to convert the radius of two-way radio B from kilometers to miles.
11.27 km × 0.62137 mi/km = 7.00 miles
Therefore, the scale factor relationship between the radio coverages is:
5 miles (radius of two-way radio A) : 7 miles (radius of two-way radio B)
or
1 : 1.4