Question

A couple of two-way radios were purchased from different stores. Two-way radio A can reach 3 miles in any direction. Two-way radio B can reach 6.44 kilometers in any direction.

Part A: How many square miles does two-way radio A cover? Use 3.14 for π and round to the nearest whole number. Show every step of your work.

Part B: How many square kilometers does two-way radio B cover? Use 3.14 for π and round to the nearest whole number. 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

Answer:

Step-by-step explanation:

Part A - 28.26 sq miles

Part B - 130.173 sq miles

Part C - 72.579 sq miles

Part D - 3.45 times

Answer 2

Answer:

A. 28 square miles

B. 130 square kilometer

C. two way radio B has larger area

D. 1.33

Step-by-step explanation:

Let's go through each part step by step:

Part A:

For a circle with radius $r$, the area ($A$) is given by the formula $A = \pi r^2$.

Given that two-way radio A can reach 3 miles in any direction, the radius ($r$) is 3 miles.

$A = \pi \times (3)^2$

$A = \pi \times 9$

$A \approx 3.14 \times 9$

$A \approx 28.26$

So, two-way radio A covers approximately 28 square miles.

Part B:

For two-way radio B, it reaches 6.44 kilometers in any direction. The radius ($r$) is 6.44 kilometers.

Area:

$A = \pi \times (6.44)^2$

$A = \pi \times 41.4736$

$A \approx 3.14 \times 41.4736$

$A \approx 130.227104$

So, two-way radio B covers approximately 130 square kilometers.

Part C:

Given that 1 mile is equal to 1.61 kilometers, we can convert the radius of two-way radio A to kilometers.

$3 \textsf{ miles} \times 1.61 \textsf{ km/mile} \approx 4.83 \textsf{ kilometers}$

Now, we can compare the areas:

- Area of two-way radio A (in kilometers) $\approx \pi \times (4.83)^2= 72.3456$

- Area of two-way radio B $\approx \pi \times (6.44)^2 = 130.227104$

By comparing the two areas to determine two way radio B covers the larger area.

Part D:

The scale factor relationship between the radio coverages can be determined by comparing the radii. The scale factor ($k$) is given by:

$k = \dfrac{\textsf{radius of radio B}}{\textsf{radius of radio A}}$

$k = \dfrac{6.44 \textsf{ km}}{4.83 \textsf{ km}}$

$k \approx 1.33$

So, the scale factor between the radio coverages is approximately 1.33. This implies that the radius of two-way radio B is 1.33 times the radius of two-way radio A.