Question

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

Answer 1

9.74 square inches, `approx` 10 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=(1/2)thetar^2`

A=area of the sector
`theta`= the central angle in radians
`r^2` the radius of the circle, squared.

Now to convert between degrees and radians we use:

Radians=`(pi)/(180) times` degrees

So 31 degrees is equal to:
`(31pi)/(180) approx 0.541... rad`

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:

`A=(1/2) times (0.541) times (6)^2`

`A= 9.74 approx 10`

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.