Find Area and Find r?

The letter A denotes the area of the sector of a circle of radius r formed by the central angle theta. Find the missing quantity. Round answers to three decimal places.





(1) r = 100 feet, theta 2 radians, find A.





(2) theta = (1/4) radians, A = 6cm, find r

Find Area and Find r?
(1) There are 2(pi) radians in a circle. Therefore, a sector of 2 radians with a radius of 100 feet would represent an area (using pi(r^2) as the area of a full circle) of





(pi)(100^2)(2/(2(pi))) = 10000 square feet





(2) In this case, we are given the area for a sector. 6 = (pi)(r^2)(.25/(2(pi)) represents the sector area; now we can solve for r.





Simplifying gives





r^2 = 48; r=Sqrt(48) = 6.928 cm.
Reply:The area of sector in a circle with radius 'r' with central angle 'theta' radians is given by


A = 0.5 x r^2 x (theta) ['theta' is in radians]





1) A = 0.5 x 100^2 x 2 = 10000 sq ft





2) 6 = 0.5 x r^2 x (1/4) [A = 6 sq cm]


r^2 = 48


r = √48 = 4√3 cm