Question

Use the fact that the length of an arc intercepted by an angle is proportional to the radius to find the arc length given the circle area A = 25π cm2 and Θ = straight pi over 4 Your answer: 20straight pi fraction numerator 5 pi over denominator 4 end fraction fraction numerator 4 pi over denominator 5 end fraction fraction numerator 10 pi over denominator 4 end fraction

Answer 1

s = 5/4 pi

Explanation:

A = 25π cm2

Theta = pi/4

A = pi r^2 = 25 pi

Divide each side by pi

r^2 = 25

Taking the square root of each side

sqrt(r^2) = sqrt(25)

r = 5

The arc length is

s = r * theta where theta is in radians

s = 5 * pi/4

s = 5/4 pi