Question

This exercise involves the formula for the area of a circular sector. the area of a sector of a circle with a central angle of 170° is 70 m2. find the radius of the circle. (round your answer to one decimal place.) m

Answer 1

The formula of interest is
A = (1/2)r²·θ
You have A = 70 m², θ = 170° = 17π/18 rad. Then the radius is found from
70 m² = (1/2)r²(17π/18)
(36·70 m²)/(17π) = r²
r ≈ √47.18476 m
r ≈ 6.9 m

Answer 2

Hi there!

• A = 70 m²
• ϴ = 170° = $\dfrac {17\pi}{18}$ rad.

According to th' question :-

Area of Sector = $\dfrac {1}{2}$r².ϴ

70 m² = $\dfrac {1}{2}$r². $\dfrac {17\pi}{18}$

r² = $\dfrac {36.70}{17\pi}$ m²

r ≈ $\sqrt {47. 18476}$ m

r ≈ 6.9 m

Hence,
Th' radius of circle, r = 6.9 m


~ Hope it helps!