Question #5e822

1 Answer
Mar 15, 2017

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*3inches*3inches

A = 9pisquare inches = just under 28.3square 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 = 9pisquare 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 2.8square inches.

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