circles and thier components

Asector  = (1/2) r^2 (theta in radians)

75 = (1/2) r^2 (1.5 pi)

75 = (3/4)pi [r^2]    

75  = [.75)pi  [r^2]    divide both sides by .75pi

75 / [ .75 pi]  = r^2    

100/pi  = r^2       take the square root of both sides

10/ sqrt(pi)  = r  = about 5.64 cm

270 is 3/4ths of a circle. 75 is 3/4ths of 100, so the whole circle is 100 square centimeters. pi*r^2 determines the area of a circle, so the answer is sqrt(100/pi), or 10sqrt(1/pi). The square root of pi is about 0.5641. Multiply by 10 and you get 5.64 (rounded) as the answer.