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In Hoboken, NJ, Benny Tudino's Pizzeria offers a 32" diameter House Pie. A new server inadvertently cuts me a slice of pizza with a 38° central angle. a. How many inches of crust is on this slice? b. How much pizza am I about to eat?

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Answer:

Explanation:

a. To determine how many inches of crust is on this slice, we need to use the formula for the circumference of a circle.Circumference of the circle= π × diameterSince the diameter of the 32" pie is given, we can find the circumference as:Circumference of the pie = π × diameter= π × 32= 100.53 inchesSince the central angle of the slice is given as 38°, we can find the fraction of the circumference that this angle represents as:Fraction of the circumference = Central angle/360°= 38/360= 0.1056Therefore, the length of the crust on this slice is the fraction of the circumference times the diameter of the pie:Length of the crust = Fraction of the circumference × Diameter= 0.1056 × 32= 3.38 inchesTherefore, the length of the crust on this slice is approximately 3.38 inches.b. To find how much pizza you are about to eat, we need to use the formula for the area of a circle.Area of the pie = π × (radius)^2= π × (16)^2= 804.25 square inchesSince the central angle of the slice is given as 38°, we can find the fraction of the area that this angle represents as:Fraction of the area = Central angle/360°= 38/360= 0.1056Therefore, the area of the slice is the fraction of the area times the total area of the pie:Area of the slice = Fraction of the area × Area of the pie= 0.1056 × 804.25= 84.89 square inchesTherefore, you are about to eat approximately 84.89 square inches of pizza.

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