Question

The diameter of a circle is 12 feet. What is the area of a sector bounded by a 70° arc ?

Answer 1

Answer: 7π

Explanation:

Because the sector is bounded by a 70-degree arc, you know that the angle formed inside the circle that creates the sector is 70 degrees as well.

You know that the diameter is 12 feet, and half the diameter is the radius. If you divide the diameter by 2, you get 6 feet as your radius. Once you have the radius, you can find your circle's area.

π · radius² is your circle area. Therefore, your circle area should be 36π.

Once you have your total circle area, you can set up a proportion. The ratio of the sector area to the total area of the circle is equivalent to the ratio of the sector angle to the total angle of a circle. In a circle, there are 360 degrees.

Therefore,
`(x)/(36\pi)` is equivalent to
`(70)/(360)`. If you cross multiply, you can find what x (your sector area) is.

You should come up with 7π as your answer in terms of pi.