Answer:
[tex] r = 6\sqrt{3} [/tex]
Step-by-step explanation:
Area of the shaded section = θ/360*πr²
Area = 15π m²
θ = 360° - 310° = 50°
r = ??
If in the values into the equation and solve for r
15π = 50/360 × π × r²
[tex] 15 \pi = \frac{5 * \pi * r^2}{36} [/tex]
Multiply both sides by 36
[tex] 15 \pi * 36 = \frac{5\pi * r^2}{36}*36 [/tex]
[tex] 540 \pi = 5\pi * r^2[/tex]
Divide both sides by 5π
[tex] \frac{540 \pi}{5\pi} = \frac{5\pi * r^2}{5\pi} [/tex]
[tex] 108 = r^2 [/tex]
[tex] r = \sqrt{108} [/tex]
[tex] r = \sqrt{36*3} [/tex]
[tex] r = 6\sqrt{3} [/tex]
