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

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.