a. To determine whether the crust will be thicker or thinner when using the circular pan, we need to compare the surface area of the rectangular pan to the circular pan.
The surface area of a rectangle is calculated by multiplying the length and the width. In this case, the surface area of the rectangular pan is 10 in. * 14 in. = 140 sq. in.
The surface area of a circle is calculated by multiplying the square of the radius by the constant pi (π). The radius is half the diameter, so the radius of the circular pan is 12 in. / 2 = 6 in. Therefore, the surface area of the circular pan is 6 in. * 6 in. * π = 36π sq. in.
Comparing the surface areas, we have 140 sq. in. for the rectangular pan and 36Ï€ sq. in. for the circular pan. Since 140 > 36Ï€, the rectangular pan has a larger surface area, which means the crust will be thicker when using the circular pan.
b. To achieve the same thickness as the 10 in. by 14 in. pizza in the recipe, we need to find the diameter of a circular pan that has a surface area equivalent to 140 sq. in.
The surface area of a circle is given by the formula: A = πr^2, where A represents the surface area and r represents the radius.
We want to find the diameter, which is twice the radius. So, we can rewrite the formula as: A = π(d/2)^2, where d represents the diameter.
We can rearrange the equation to solve for the diameter: d = √(4A/π).
Plugging in the value of A as 140 sq. in., we get: d = √(4*140/π) ≈ √560/π ≈ 10.64 in.
Therefore, to make a round pizza with the same thickness, Jake will need a pan with a diameter of approximately 10.64 inches.
As for whether Jake is likely to find such a pan, it may not be a standard size readily available in most stores. However, there are specialty cooking stores or online platforms where he might be able to find a pan with a diameter close to 10.64 inches. It may require some searching or possibly purchasing a custom-made pan.