What is the approximate area of a 70 degree sector of a circle with the radius of 8 inches?

Answer 1

The area of a circle is pi times the radius squared; 22/7 is a good approximation of pi. The fraction 70 degrees out of 360 is equal to 7/36; this is about the same as 7/35, which is one-fifth exactly. However, by writing the fractions in the expression:

(22/7) x (7/36) x 64

we can see that the 7s cancel out, and the expression is reduced to

(22/36) x 64

We can then simplify this by
(22 x 64)/36

The top part of this is about the same as 20 x 65, which equals 1300. We have then further reduced the approximation to

1300/36

36 squared is 1296, just under 1300, so we can finally appproximate this with 36 square inches, our final answer.

By comparing this to the unrounded and exact answer, 39.095375, we are not too far off - only an 8% difference - and the approximation would only have taken around a fifth of the time that an exact calculation would taken, unless you used a calculator.