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

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

circle sector area = half of radius squared times angle when measured in radians

19 = .5(r^2)(5pi/12)

r^2 = 19/.5(5pi/12)

radius = sqr(19/.5(5pi/12)) meters = about

15.37 meters

Answer 2

Make a proportion.

Area of sector = central angle

Area of circle central angle of entire circle

19 = 5π/12

π r^2. 2 π

Solve for r. Start by cross multiplying.

(19) (2 π) = (5π/12) (π r²) Divide both sides by π

(19) (2). = (5/12)(π r²) Multiply both sides by 12/5π

(19) (2) (12) = r² Take square root of both sides.

5π

r = 5.4

Now let's check it.

If the radius is 5.4, then the area of the entire circle is 5.4² π. or 91.6 m²

Is Area of sector = central angle

Area of circle central angle of entire circle

19 = 5 π /12 ???

91.6 2π

38 π = 91.6. (5 π /12)

38 π. = 38 π. YES!!

Answer 3

19 = (5π / 12)(r²)

Can you solve for r and answer?