Question

Find the area of the circle that contains the sector described below. Round to the nearest tenth, if necessary.

One sector has an area of 210 square centimeters and an arc measure of 30°.


_____________ cm squared

Answer 1

The area of the circle is 2520 cm²

Explanation:

The area of an arc is given by the following formula:

arc area = pi*r²(angle/360)

In this case we have the area and the angle and we want to find r, so we have:

210 = pi*r²*(30/360)

210 = pi*r²*(1/12)

210*12 = pi*r²

pi*r² = 210*12

r² = 2520/pi

r = sqrt(2520/pi)

r = 28.3221

The area of the circle that has this arc is given by:

area = pi*r²

area = pi*(28.3221)² = 2520 cm²