Question

Find the radius of the circle below. Round your answer to the nearest tenth.

Answer 1

5.8 cm

Explanation:

Area of the shaded sector of the circle = 31.2 cm²

Angle (θ) of the minor sector = 360 - 256 = 104°

Are of sector of a circle is given as, θ/360*πr²

Therefore:

`(104)/(360)*3.142*r^2 = 31.2`

`0.29*3.142*r^2 = 31.2`

`0.91*r^2 = 31.2`

Divide both sides by 0.91

`(0.91*r^2)/(0.91) = (31.2)/(0.91)`

`r^2 = (31.2)/(0.91)`

`r^2 = 34.286`

`r = √(34.286)`

`r = 5.8` (nearest tenth)