10) a. A recipe for pizza dough says to use a 10 in. by 14 in. rectangular pan. Jake only has a circular pan with a 12 in. diameter. If Jake makes the pizza in his circular pan, will the crust be thicker or thinner? Explain.
b. Suppose Jake wants to make a round pizza that is exactly the same thickness as the 10 in. by 14 in. pizza in the recipe. What will the diameter of the pan have to be? Is Jake likey to find such a pan? Why or Why not?
I am so confused, please help me!
10a The pizza with the larger arera will have the thinner crust, because it has to be spread out more. Compare the areas.
10a. The pizza with the larger arera will have the thinner crust, because it has to be spread out more. Compare the areas.
10b. Require that the circular pan area be 140 square inches. Set 140 equal to (pi/4)D^2 and solve for D. Have you ever heard of a pizza pan of that size?
a. To determine whether the crust will be thicker or thinner in Jake's circular pan compared to the rectangular pan, we need to consider the difference in their shapes and sizes.
1. First, let's calculate the area of the rectangular pan:
Area = Length x Width = 10 in. x 14 in. = 140 in².
2. Now, let's calculate the area of the circular pan:
Area = πr², where r is the radius of the circular pan. We know that the diameter (d) is given as 12 in., and the radius (r) is half the diameter.
Substituting the values, we get:
Area = π(6 in.)² = 36π in² ≈ 113.1 in².
Comparing the areas, we can see that the rectangular pan has a larger area (140 in²) compared to the circular pan (113.1 in²). Hence, when Jake makes the pizza in his circular pan, the crust will be thicker because the same amount of dough will be spread over a smaller area.
b. To find the diameter of the pan needed to make a round pizza with the same thickness as the 10 in. by 14 in. pizza, we need to consider the surface area of both pizzas.
1. Calculate the surface area of the rectangular pizza:
Surface Area = Length x Width = 10 in. x 14 in. = 140 in².
2. We want to find the diameter of a circular pan that will have the same surface area as the rectangular pan. The surface area of a circle is given by:
Surface Area = πr², where r is the radius.
Substituting the known values (140 in²) into the equation, we get:
140 in² = πr²
Solving for r, we have:
r² = 140 in² / π
r ≈ √(140 in² / π)
r ≈ 6.00 in
3. Finally, to find the diameter of the circular pan, multiply the radius by 2:
Diameter = 2r = 2 x 6.00 in = 12.00 in.
Therefore, to make a round pizza with the same thickness as the 10 in. by 14 in. rectangular pizza, Jake would need a circular pan with a 12 in. diameter. Luckily, Jake already has a circular pan with a 12 in. diameter, so he is likely to find such a pan.