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

1 Answer
Apr 6, 2018

9.74 square inches, #approx# 10 square inches


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
#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.


#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.