Question

Points A and B lie on a circle centered at point O. If OA = 5 and length of ABowncircumference=14, what is the area of sector AOB? Use the value π = 3.14, and choose the closest answer.

Answer 1

From Geometry, we know that, if an arc (i.e., part of circumference of a circle) of length s subtends an angle of measure #theta# (in radian) at the centre of the circle with radius r, then,\ Here, we are given that, \ \[:. \theta=s/r=14/5=2.8radian.\] Now, area of sector\[AOB=1/2*r ^{2}\theta=(0.5)(5^{2})(2.8)=35sq.unit.\]