Question

A satellite sends signals from space to the regions that lie within the shaded portion of the Earth, as shown below. If the radius of the Earth is approximately 6000 kilometers, and the central angle the satellite creates measures 60° the part of Earth that receives signals from the satellite has an area of ____ square kilometers. Use 3.14 for T.

Answer 1

18840000 square kilometers

Step-by-step explanation

We want to find the area that will receive the signal, that is the area of the shaded sector.

To do this, we apply the formula for the area of a sector of a circle:

`\begin{gathered} A=(\theta)/(360)\cdot\pi\cdot r^2 \\ \text{where} \\ \theta=\text{ central angle of sector} \\ r\text{ = radius of circle} \end{gathered}`

We are given the central angle and the radius of the circle.

Therefore, the area of Earth that receives the signals is:

`\begin{gathered} A=(60)/(360)\cdot3.14\cdot6000^2 \\ A=18840000\text{ square kilometers} \end{gathered}`

That is the area of Earth that receives the signals.