The area of a sector of a circle with a central angle of 5𝜋/12 rad is 19 m2. Find the radius of the circle.

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 5𝜋/12 rad is 19 m². Find the radius of the circle. (Round your answer to one decimal place.)

 m

Answer 1

A = (θ / 2)r², where θ is the central angle measured in radians

Substitute values and solve for r.

Answer 2

The proportion of the total area that is the area of a sector is equal to the fraction of the central angle of the sector is to 2π (the whole circle central angle)

19 = (5π/12)/(2π) * πr² = (5/24)πr²

Now solve for r

Sqrt(19*24/(5π)) = r