# 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.)

Apr 6, 2018

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:

$A = \left(\frac{1}{2}\right) \theta {r}^{2}$

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=$\frac{\pi}{180} \times$ degrees

So 31 degrees is equal to:
$\frac{31 \pi}{180} \approx 0.541 \ldots r a d$

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:

$A = \left(\frac{1}{2}\right) \times \left(0.541\right) \times {\left(6\right)}^{2}$

$A = 9.74 \approx 10$

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.