Question

Question #5e822

Answer 1

Area of the entire circle with radius `3` inches is `9pi` or `28.3` square inches.
Area of the sector enclosed by a central angle of `36` degrees is `(9pi)/10` or `2.8` square inches.

Explanation:

This question is ambiguous and can result in several answers.

If it is only the area of the circle that is required, information about the central angle is irrelevant and area is:

`A = pi r^2`

`A = pi*3`inches`*3`inches

`A = 9pi`square inches`= just under 28.3`square inches

If the central angle is relevant, and it is the area of the enclosed sector required, the area can be found by:

Total area: `A = 9pi`square inches,

But the sector enclosed by `36` degrees is `36/360` or `1/10` of the entire circle.

Then the area enclosed by the sector is: `A = 9pi * 1/10 = (9pi)/10`, or `just over 2.8`square inches.

There is also the possibility that the area of the circle minus the enclosed sector is required, which equates to `9*(9pi)/10 = 8.1pi`square inches.

Note that answers where `pi` is not translated to its decimal form are more accurate. This becomes important when repeatedly computing with `pi` in an answer, so do not change to the decimal form until the last step if necessary.

Happy `pi` day, 3/14/2017!