Pieces of the Pie

Dr. Jason Gershman

Parts of Circles

• Sometimes, the whole circle is not needed or not available and you can only have part of a circle.

• Find the area of a semicircle of radius 12.

Sectors

• Find the areas of the sector Shaded in green to the right if The radius is 10 feet and the Central angle of the sector is30 degrees?What if the radius is increased to 20 feet?What if the central angle is increased to 60Degrees?

Pizza

• Pizza is often circular shape and the size of the pizza is the length of the diameter (crust included). A 14 inch pizza is one with a 14 inch diameter. Find the area of a 14 inch pizza.

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Slice of Pizza

• Normally pizza is sliced into 8 sectors each measuring a central angle of 45 degrees.

• Find the area of one slice of pizza from a 12 inch pizza.

• Find the perimeter of this slice of pizza.

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Removing the crust

• Some people do not like to eat the crust, the outer edge of the pizza with no cheese or sauce. Suppose that a 14 inch pizza has an area of crust which is 13π. Find the radius of the saucy/cheesy inner concentric circle of pizza.

• What percentage of the pizza above is crust?

Optimization of Pizza

• Suppose that crust costs 2 cents per square inch to produce and the rest of the pizza costs 5 cents per square inch to produce. How much does this pizza cost to produce.

• If this restaurant charges $17 for this pizza, how much profit do they make per pie?

Caloric Intake

• The pizza shown at right is half pineapple/sausage and half olives/peppers.

• Suppose that for this 10 inch pizza, the pineapple/sausage part is 15 calories per square inch and olives/peppers is 11 calories per square inch.

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Caloric Intake

• Find the total caloric intake if you ate the entire pizza.

• Find the caloric intake if you ate 3 out of 4 slices of the pineapple/sausage 2 out of 4 slices of the olives/peppers.

• Find the maximum number of slices of pizza you could eat if you were only allowed to eat 500 calories. How many of each type of pizza are included in the maximum.

Dessert

• After all of that pizza, you need dessert.

• Suppose that there are 10 blueberries per square inch and you used an entire box of 360 blueberries to make this pie, find the diameter of this pie (rounded to two decimal places.)

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Best Value

• A newspaper advertisement for a major pizza chain advertises the following specials:– 3 medium (12 inch) pizzas for $15– 2 large (14 inch) pizzas for $13– 2 extra large (16 inch) pizzas for $19– 6 personal pizzas (6 inch) pizzas for $20.

• Assume the diameter without the crust is two inches fewer than advertised, find the actually area of pizza you receive in each scenario. Which deal is best to get the most pizzas per dollar?

Your Own Problem

• Pose and solve your own “pizza problem” involving areas and perimeters of circles and sectors.