Answer:
r ≈ 5.26 cm
Step-by-step explanation:
The area (A) of the bigger part is calculated as
A = area of circle × fraction of circle
The angle subtended at the centre by the bigger part = 360° - 165° = 195°
A = πr² × [tex]\frac{195}{360}[/tex]
Here A = 47, thus
πr² × [tex]\frac{195}{360}[/tex] = 47 ( multiply both sides by 360 to clear the fraction )
195πr² = 16920 ( divide both sides by 195π )
r² = [tex]\frac{16920}{195\pi }[/tex] ( take the square root of both sides )
r = [tex]\sqrt{\frac{16920}{195\pi } }[/tex] ≈ 5.26 cm ( to 2 dec. places )
