Question 1171561: An 18-inch pizza is to be equally divided among the group of 8 people.
a. What is the central angle created by three cuts of pizza?
b. Determine the arc length for the three cuts of pizza.
c. If a cut of pizza had an arc length of 9π/4, what is the area of the cut of pizza to the nearest tenth of a square inch?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 18 inch diameter pizza has a radius of 18/2 = 9 inches.
circumference of that pizza is 2 * pi * 9 = 18 * pi = 56.54866776 inches.
area of that pizza is pi * 9^2 = 81 * pi = 254.4690049 square inches.
central angle of the whole pizza is 360 degrees.
since there are 8 slices of pie in that pizza, than the arc length of one slice of pizza is 18 * pi / 8 and the area of one slice of pizza is 81 * pi / 8 and the central angle formed by one slice of pizza is 360 / 8.
answers to your questions are:
a.
central angle formed by 3 slices of pizza is 3 * 360 / 8 = 135 degrees.
b.
arc length of 3 slices of pizza is 3 * 18 * pi / 8 = 6.75 * pi = 21.20575041 inches.
c.
if a cut of pizza had an arc length of 9pi/4, then the arc length of that pizza is the same as the arc length of one slice of pizza, because 9 * pi / 4 = 18 * pi / 8 = 2.225 * pi = 7.068583471 inches.
the area of that slice of pizza would be 81 * pi / 8 = 10.125 * pi = 31.80862562 square inches.
round to nearest tenth of a square inch to get 31.8 square inches.
those are you answers.
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