Question

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

Answer 1

Answer:

5.8 cm

Step-by-step 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:

$\frac{104}{360}*3.142*r^2 = 31.2$

$0.29*3.142*r^2 = 31.2$

$0.91*r^2 = 31.2$

Divide both sides by 0.91

$\frac{0.91*r^2}{0.91} = \frac{31.2}{0.91}$

$r^2 = \frac{31.2}{0.91}$

$r^2 = 34.286$

$r = \sqrt{34.286}$

$r = 5.8$ (nearest tenth)