Mathematics, 01.07.2019 16:10 katey3809

Big bob's pizza is having a special on pizza and is offering two different choices: choice #1: one slice of pizza from a pizza with a 22 inch diameter and is cut into 8 slices. the cost is $4.95. choice #2: an entire personal-size pizza that has a diameter of 6 inches. the cost is $3.75. which choice will give you more pizza for your money? justify your answer using numbers and words.

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Answer from: jamie316

The special at Big Bob's Pizza which will give you more pizza for your money is Choice #1. Per square inch, Choice #1 will cost less and give more overall pizza at $0.10 a square inch then Choice #2 at $0.13 per square inch. You can find more pizza for your money, by using the area formula for a circle for each pizza and finding the price per square inch of each serving. This is called a unit rate and is the cost per unit.

Further Explanation

a. Find the radius of each pizza.

Since a pizza is a circle shape, it has a diameter and radius. The diameter is the distance across the pizza and the radius is half the diameter. We use the radius to find the area.

Choice #1: One slice of a pizza with a 22 inch diameter and is cut into 8 slices. Since the diameter is the distance across the pizza, 22 inch diameter means the pizza is 22 inches wide. The area formula uses the radius or half the diameter. The radius of choice #1 is 11 inches.Choice #2: An entire personal-size pizza that has a diameter of 6 inches. Here the radius is half of 6 inches. The radius of choice #2 is 3 inches.

b. Find the area of each pizza using $A = \pi r^{2}$ .

Choice #1: Substitute r = 11 into the formula then divide by 8 to find the area of one slice or serving.

$A = \pi r^{2} \\A = \pi (11)^{2} \\A = 121\pi \\A= 379.94$

The area of one slice is $\frac{379.94}{8} = 47.49.$

Choice #2: Substitute r = 3 into the formula. This is a personal pizza so the entire pizza is a serving.

$A = \pi r^{2} \\A = \pi (3)^{2} \\A = 9\pi \\A= 28.26$

c. Divide each area by the price.

The cost of Choice #1 is $4.95. Since the serving size is 1 slice, use the area of the slice 47.49. Divide it into the price to find the cost per square inch of one serving.

$\frac{4.95}{47.49} = 0.10$

The cost of Choice#2 is $ 3.75. Since the serving serving size is the entire personal pizza, use the area of the pizza 28.26.

$\frac{3.75}{28.26} = 0.13$

Learn More Area and Circumference of a Circle Application: Cost per unit: Answer Details

Grade: 8th Grade

Subject: Geometry

Chapter: Applications for Area of Shapes

Keywords: circle, area, radius, diameter, cost, unit rate

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