Question 631700
area of a circle is equal to pi*r^2.
area of a sector is equal to x/360 * the area of the circle.
this is equal to x/360- * pi*r^2.
x is equal to the number of degrees in the sector.
a sector is the area formed by the central angles and the arc formed on the circumference of the circle.
your angle is equal to pi/2.
this is the measure of your angle in radians.
to convert from radians to degrees, you have to multiply the radians by 180 / pi.
pi / 2 * 180 / pi = (pi * 180) / (2 * pi) = 180/2 = 90 degrees.
the radius of the circle is equal to 10 (given).
pi is always equal to 3.141592654
bottom line is:
the area of your sector is equal to:
90/360 * pi*r^2 which is equal to:
1/4 * pi*(10^2) which is equal to:
1/4 * pi*100 which is equal to:
78.53981634 units.
the area of the circle is equal to pi*r^2 which is equal to 100*pi which is equal to 314.1592654.
the area of your sector is 1/4 times this which makes the area of your sector equal to 78.53981634
it all checks out.
a diagram of your circle and the sector in question is shown below:
<img src = "http://theo.x10hosting.com/2012/paint_0016.jpg" alt = "$$$$" />