We are asked to find the area of a circular sector subtended by a central angle of 64 degrees, in a circle of radius 9 in.
We recall that the area of a FULL circle is given by the expression:
pi * R^2 where R is the radius of the circle.
Then all we need previous to the area calculation is to understand that such calculation is for a 360 degree angle, then we can use proportions to find the area we need
64 degrees / 360 degrees = 8/45
That means that the area of our sector should be 8/45 times the area of the full circle
Full circle area = pi 9^2 in^2 which is approximately: 254.47 in^2
Then (8/45) * 254.47 in^2 = 45.24 in^2 (Are of our sector
This is a result rounded to TWO decimals.
Please let me know if your problem requires more or less decimals for the rounding.