Help Sector area problem!?

Question

A portion of a road curve is a circular arc with a radius of 186.2 metres to the centre line of the road and a central angle of 75.8 degrees. If the road is 22.5metres wide, determine the surface area of the curved section of the roadway

Answer is supposed to be 5543 meters squared...anyone know how to get it?

Answer 1

Take the area of the outside curve - area of inside curve.

First, you need the radius. The radius is given to the centre line, so you take the radius of the center line +/- the width of the road:
Outside radius = 186.2 m - 22.5/2 m = 208.45 m
Inside radius = 186.2 m - 22.5/2 m = 163.95 m

Now that you have the radius, find the area of the section:
Area = πr^2 * (75.8/360 : ratio of angle to full circle)
Outside area = π * (208.45m)^2 * 0.210556 = 28742 m^2
Inside area = π * (163.95m)^2 * 0.210556 = 17780 m^2

Now that you have the areas, subtract:
Outside area - Inside area = 28742 m^2 - 17780 m^2 = 10962 m^2 (solution!)

Answer 2

permit the arc BC subtends an attitude O on the midsection A of the circle. Then O=a million/9 rad, the part of the international= (a million/2)(6^2)(a million/9)= 2 sq. gadgets be conscious that the part of a sector= (a million/2)(radius^2)(attitude)