# 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.)

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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.