Raymond B. answered • 10/11/20
Math, microeconomics or criminal justice
diameter = 20 means the radius =10. d=2r, 20=2r.
area of a sector of a circle with central angle 70 = 70/360 times area of the circle
= 7/36 x pi(10^2) = 700/36 pi = 350/18 pi = 175/9 pi = about 19.444 x 3.14159 = about 60.9
area of the circle is 100pi = 314.159. 70/360 = 7/36 = a little less than 1/5. 1/5 of 314 is about 63 = a rough approximation. 60.9 looks about right.
none of the a), b), c), or d) come close. If you had to choose a "best" answer 14.10 is closest to 60.9.
Or maybe the "70" refers to radians instead of degrees, but that seems unlikely as it means the "segment" or sector is 70/2pi times the area of the circle. 70/2pi x 100pi = 70x50 = 3500, That is also unlike any of the alternatives. "Best" answer then would be d) as it's closest, even though very far off. IF you multiply d) by 2.5 you get very close to 3500. that's about the only connection that you might find. The 141's in the alternatives look similar to the square root of 2 = 1.41, but that also seems unrelated to any method of solving this problem. Maybe the solutions got miscopied from another problem.
