Respuesta :
Answer:
Choice #1 is better
Step-by-step explanation:
To find the solution to this problem, we have to compute the are in each case, and divide each value by the corresponding cost in order to find the cost per square. The lower the cost, the better the offer because it will give you more pizza for your money Thus:
CHOICE 1:
Here the offer of Big Bob’s Pizza gives one slice of pizza from a pizza with a 22 inches diameter (then the radius is 11 inches) and is cut into 8 slices, so the area for the first entire pizza is:
[tex]A_{1}=\pi r^2=\pi(11)^2 \\ \\ A_{1}=121 \pi in^2[/tex]
Each slice has an area of:
[tex]A_{slice}=\frac{121 \pi}{8} \\ \\ A_{slice}=47.51in^2[/tex]
Finally, the cost per square inch is:
[tex]C=\frac{4.95\$}{47.51in^2}=0.10\$[/tex]
CHOICE 2:
Here the offer of Big Bob’s Pizza gives: An entire personal-size pizza that has a diameter of 6 inches (then the radius is 3 inches), so the area for the entire pizza is:
[tex]A_{2}=\pi r^2=\pi(3)^2 \\ \\ A_{2}=28.27 in^2[/tex]
Finally, the cost per square inch is:
[tex]C=\frac{3.75\$}{28.27in^2}=0.13\$[/tex]
CONCLUSION: Choice #1 gives you more pizza for your money because the cost per square inch is less than the other option.
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 [tex]A = \pi r^{2}[/tex].
- Choice #1: Substitute r = 11 into the formula then divide by 8 to find the area of one slice or serving.
[tex]A = \pi r^{2} \\A = \pi (11)^{2} \\A = 121\pi \\A= 379.94[/tex]
The area of one slice is [tex]\frac{379.94}{8} = 47.49.[/tex]
- Choice #2: Substitute r = 3 into the formula. This is a personal pizza so the entire pizza is a serving.
[tex]A = \pi r^{2} \\A = \pi (3)^{2} \\A = 9\pi \\A= 28.26[/tex]
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.
[tex]\frac{4.95}{47.49} = 0.10[/tex]
- 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.
[tex]\frac{3.75}{28.26} = 0.13[/tex]
Learn More
- Area and Circumference of a Circle Application: https://brainly.com/question/3519879
- Cost per unit: https://brainly.com/question/11521316
Answer Details
Grade: 8th Grade
Subject: Geometry
Chapter: Applications for Area of Shapes
Keywords: circle, area, radius, diameter, cost, unit rate
Read more on Brainly.com - https://brainly.com/question/12878495
