A radio station has a broadcast area in the shape of a circle with equation x² + y² = 5,625, where the constant represents square miles.
Graph the equation and state the radius in miles.
What is the area of the region in which the broadcast from the station can be picked up?

Solution:

Give, a radio station has a broadcast area in the shape of a circle with equation x² + y² = 5625 --- (1)

We have to find the radius in miles and area of the region.

The general equation of the circle is x² + y² = r² --- (2)

Where r is the radius of the circle.

By comparing (1) and (2),

r² = 5625

Taking square root,

r = 75

Therefore, the radius of the circle is 75 miles.

Area of the broadcast region = πr²

= π(5625)

Take π = 3.14

So, area = 3.14(5625)

= 17671 square miles.

Therefore, the area of the broadcast region is 17671 square miles.

Therefore, the radius is 75 miles and the area is 17671 square miles.

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A radio station has a broadcast area in the shape of a circle with equation x² + y² = 5,625, where the constant represents square miles.
Graph the equation and state the radius in miles.
What is the area of the region in which the broadcast from the station can be picked up?

Summary:

A radio station has a broadcast area in the shape of a circle with equation x² + y² = 5625, where the constant represents square miles. The radius is 75 miles. The area of the region in which the broadcast from the station can be picked up is 17671 square miles.