Question

The area of a sector of a circle with a central angle of 170° is 70 m 2. find the radius of the circle. (round your answer to one decimal place.)

Answer 1

The area of a sector of a circle is $A= \frac{ \theta }{360} * \pi r^2$.  We have everything but the radius to fill in there, so let's do it: $70= \frac{170}{360} * \pi r^2$.  To make it easy, cross out the last 0 in both the 170 and the 360, and then multiply both sides by 36 to get $2520=17 \pi r^2$.  Divide both sides by 17pi and you have 47.1847596=r^2 and r = 6.9

Answer 2

Area of a circle = πr²

Area of a sector = πr²*(α/360⁰)

70 = πr² * 170/360

r² = (70*360)/(170*π)

r = √(70*360)/(170*π) ≈ 6.9 m

r ≈ 6.9 m