Points r and s lie on circle o with radius 2, and the area of sector ros is pi/2. what fraction of the area od the circle is the area of sector ros? explain.

Step-by-step

Yes, there is a way.  However, the equation involved is much simpler if we use radians for angles.

A complete circle (360 degrees) equals 2pi radians.

For example, 90 degrees equals 1/4 of 2pi = pi/2 radians, etc.

The area of a sector of radius r subtending an angle of alpha has an area of Area of sector = r^2(alpha)/2

which means that the area of a complete circle (angle alpha=2pi)

Area of circle = r^2(2pi)/2 = pi (r^2)  as we all know.

So for given, A=pi/2

Area of sector = r^2(alpha)/2 = 2(alpha) = pi/2, we solve for

alpha = pi/2/2 = pi/4  (which is same as 45 degrees).

Therefore the fraction of the sector

= (pi/4)/ (pi/2) = 1/8

From the above, a simple formula can be found, which is dividing simply the area of the sector by the area of the circle, pi(r^2), i.e. (pi/2)/(pi(2^2))=(pi/2)/(pi/4) = 1/8

multiple all that

step-by-step explanation:

27×17