A 12 inch (in diameter) pizza is cut into various sizes. What is the area of a piece that was cut with a central angle of 31 degrees? The area of the piece of pizza is approximately ____ square inches. (Round to two decimal places as needed.)
please help
please help
1 Answer
9.74 square inches,
Explanation:
This question is best answered if we convert the 31 degrees to radians. This is because if we use radians, we can use the equations for the area of a circle sector (which a pizza slice is, pretty much) using the equation:
A=area of the sector
Now to convert between degrees and radians we use:
Radians=
So 31 degrees is equal to:
Now we simply have to plug it into the equation, as if the diameter is 12 inches, then the radius must be 6 inches.
Hence:
So the slice of pizza is 9.74 square inches to two decimal places, or 10 square inches if your round it to the nearest whole number.