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Circular Logic (RP3C GA1)

Last updated over 4 years ago

7 questions

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Question 1

1.

How much bigger is the giant pizza than the large pizza in terms of area?

Give answer as a sentence in square inches AND as a percent.
(Ex "Object 1 is 22 sq inches, or 53%, bigger than Object 2.")
Round area and percents to nearest whole number

Reminders:
Sizes: Regular 78.54 in2, 113.1 in2, 201.06 in2
A = πr2 (use 3.1416 for π)
There are 360° in a circle
Percent increase = (larger number - smaller number) ÷ smaller number
Percent decrease = (larger number - smaller number) ÷ larger number

Question 2

2.

How much smaller is the regular pizza than the large pizza in terms of area?

Give answer as a sentence in square inches AND as a percent.
(Ex "Object 1 is 22 sq inches, or 53%, bigger than Object 2.")
Round area and percents to nearest whole number

Reminders:
Sizes: Regular 78.54 in2, 113.1 in2, 201.06 in2
A = πr2 (use 3.1416 for π); Circumference = 2πr
There are 360° in a circle
Percent increase = (larger number - smaller number) ÷ smaller number
Percent decrease = (larger number - smaller number) ÷ larger numberSizes: Regular 78.54 in2, 113.1 in2, 201.06 in2

Question 3

3.

The owner sells a regular cheese pizza for $8.25. He wants to know what to charge for the large and giant sized pizzas. He wants to cover the cost of the ingredients and make a proportional amount of profit on the other two pizzas (propotional means profitability is in a constant ratio with size).

What should he charge for a large and giant cheese pizza?
Give you answer as a sentence. (ex "The owner should charge 10.50 for a large pizza and $17.75 for a giant pizza." Show your calculation for full credit.

Reminders:
Sizes: Regular 78.54 in2, 113.1 in2, 201.06 in2
A = πr2 (use 3.1416 for π); Circumference = 2πr
There are 360° in a circle
Percent increase = (larger number - smaller number) ÷ smaller number
Percent decrease = (larger number - smaller number) ÷ larger number

Question 4

4.

The owner sells pizza by the slice. He has been selling a large pizza by the slice for $1.35. Each pizza is cut into eight equal slices. The owner wants to know whether he has priced it right to make more money selling by the slice than by selling the whole pizza.

Explain to him, using mathematics, how his prices for the slices and the whole pizza compare.
Show your work for full credit.

Reminders:
Sizes: Regular 78.54 in2, 113.1 in2, 201.06 in2
A = πr2 (use 3.1416 for π); Circumference = 2πr
There are 360° in a circle
Percent increase = (larger number - smaller number) ÷ smaller number
Percent decrease = (larger number - smaller number) ÷ larger number

Question 5

5.

Now the owner wants to cut each large pizza into nine slices instead of eight. How much smaller will the slices be? He is interested in comparing the width (both angle in numbers of degrees and inches at the widest part) and the area of each slice.

Give answer as a sentence (ex "Each slice will be 2° narrower and 4 sq inches smaller.")
(tip: tap 123 then press and hold 0 to access degree symbol on iPad)
Show your work for full credit.

Reminders:
Sizes: Regular 78.54 in2, 113.1 in2, 201.06 in2
A = πr2 (use 3.1416 for π); Circumference = 2πr
There are 360° in a circle
Percent increase = (larger number - smaller number) ÷ smaller number
Percent decrease = (larger number - smaller number) ÷ larger number

Question 6

6.

The owner wants to sell the nine slices at the same price as he did when the pizza was cut into eight slices ($1.35 a slice). He wants to know how much more he will make cutting the pizzas into smaller slices. He wants to compare the prices of selling the nine slices individually with the price of selling an entire large pizza. He asks you to calculate and explain the difference in prices and amounts.

Give answer as a sentence (ex "He will make $6 more selling the 9-slice version of the Large pizza than the 8-slice version. This means he will make $20 selling 9 slices, $10 more than if he sold the whole pizza.)
Show your work fo full credit

Reminders:
Sizes: Regular 78.54 in2, 113.1 in2, 201.06 in2
A = πr2 (use 3.1416 for π); Circumference = 2πr
There are 360° in a circle
Percent increase = (larger number - smaller number) ÷ smaller number
Percent decrease = (larger number - smaller number) ÷ larger number

Question 7

7.

The owner also thinks he can save more money if he sells slices from regular sized pizzas instead of large sized pizzas. If you cut both the regular and large pizzas into nine equal slices, how much larger is a single slice from a large pizza than that of a slice from a regular pizza? Explain your answer in terms of degrees, along with width and area of the slice.

Give answer as a sentence (ex "Each slice will be 3° (1.5 in) inches narrower and 25 sq inches smaller"). Show your work for full credit.

Reminders:
Sizes: Regular 78.54 in2, 113.1 in2, 201.06 in2
A = πr2 (use 3.1416 for π); Circumference = 2πr
There are 360° in a circle
Percent increase = (larger number - smaller number) ÷ smaller number
Percent decrease = (larger number - smaller number) ÷ larger number