Proportions Math Problem: Comparing Pizza Sizes and Material Requirements

[halvizo1031]

Homework Statement

T or F? a pizza with 20cm diameter will require approximately half of the raw materials of pizza of diameter 40cm. explain your answer.

Homework Equations

The Attempt at a Solution

my thinking is this, if we take the area of both pizzas, then we get 100(pi) and 400(pi) respectively. thus, since one pizza is four times the size of the other, then it would require four times the amount of raw materials as the other. am i correct?

 

[LCKurtz]

Homework Statement

T or F? a pizza with 20cm diameter will require approximately half of the raw materials of pizza of diameter 40cm. explain your answer.

Homework Equations

The Attempt at a Solution

my thinking is this, if we take the area of both pizzas, then we get 100(pi) and 400(pi) respectively. thus, since one pizza is four times the size of the other, then it would require four times the amount of raw materials as the other. am i correct?

Looks good to me. What kind of pizza are we talking about here?

 

[Mark44]

Homework Statement

T or F? a pizza with 20cm diameter will require approximately half of the raw materials of pizza of diameter 40cm. explain your answer.

Homework Equations

The Attempt at a Solution

my thinking is this, if we take the area of both pizzas, then we get 100(pi) and 400(pi) respectively. thus, since one pizza is four times the size of the other, then it would require four times the amount of raw materials as the other. am i correct?

Yes. If you double the diameter of a circle, you don't double its area: you quadruple it. Don't forget to include your answer, T or F.

 

[halvizo1031]

now the second part of this question says that suppose that the price of each pizza will be directly proportional to the amount of raw materials you use. if you were to model your pricing structure as "price as a function of diameter", then would you expect that model to be linear, quadratic, or other?

wouldn't this depend on what i decide to charge for each pizza? for example, if i decide to charge $1 for every inch in diameter, then my model would be linear.

 

[Char. Limit]

now the second part of this question says that suppose that the price of each pizza will be directly proportional to the amount of raw materials you use. if you were to model your pricing structure as "price as a function of diameter", then would you expect that model to be linear, quadratic, or other?

wouldn't this depend on what i decide to charge for each pizza? for example, if i decide to charge $1 for every inch in diameter, then my model would be linear.

Remember that price is directly proportional to raw materials, that is, that P=c₁M, where P is price, M is materials, and c is some constant. Now, referring to your previous problem, what's the relation between raw materials and diameter?

 

[Pengwuino]

Depends if it's a cheese pizza or not.

And the problem is implying that you charge based on the cost of the raw materials. Something with twice the amount of raw materials, you'd want to sell for twice the price.

 

[halvizo1031]

well as we doubled the diameter, the raw materials quadrupled.

 

[Char. Limit]

well as we doubled the diameter, the raw materials quadrupled.

Correct. So obviously raw materials aren't linear with diameter, and price is linear with raw materials. So what does that say about price's relationship with diameter?

 

[halvizo1031]

it seems to me that it would be quadratic.

 

[halvizo1031]

reason i say quadratic is because if a 10cm is $5, and a 20cm take four times the amount of raw materials, then it should cost four times the amount of a 10cm pizza. thus, it would cost $20.

 

[Mark44]

Yes, that's right. Something to consider is whether the sauce and toppings are the same thickness on both sizes of pizza. If they're thicker on the larger pizza, then you would need to take that into account. In this problem, though, I don't think that's a concern.