The area of a sector of a circle with a central angle of 9π/13 rad is 24 m2. Find the radius of the circle. (Round your answer to one decimal place.)

Question

The area of a sector of a circle with a central angle of 9π/13 rad is 24 m².Find the radius of the circle. (Round your answer to one decimal place.)

Answer 1

the central angle of the sector is 9∏/13=124.61538° and the area is 24 m^2

find the area of the circle by dividing 360 by 124.61538 to find how many sectors there are with this degree measure and this area measure

360/124.61538=2.888888 sectors

2.888888*24=69.333312 m^2 is the area of the circle

A=∏*r^2

69.333312=3.14159*r^2

69.333312/3.14159=r^2

r^2=22.069497

take the square root of both sides

r=4.6978184

r=4.7 m

Answer 2

9*pi/13 * R^2 = 24

pi*R^2 = 24*13/9

pi*R^2 = 8*13/3 = 104/3 = 34 and 2/3 = 34.6

r^2 = 104/(3*pi)

r = sqrt( 104/(3*pi))

= sqrt ( 104*3*pi) / (3*pi)

= sqrt( 312*pi)/(3*pi)

which is approximately 3.3218583234445861317535211196824....