Question

edward’s grandmother used to make him pannukakku when he was little. he wants to surprise her by making it himself. the recipe he found requires a 9 - in. by 13 - in. rectangular pan. edward would like to use a round cast iron pan like his grandmother does. what is the area of a 9 - in. by 13 - in. pan? 117 in.² edward has four round pans, each with a different radius. he needs to use the pan that is closest in area to the rectangular pan. which pan should edward use? a pan with a radius of 4 in. a pan with a radius of 6 in. a pan with a radius of 8 in. a pan with a radius of 10 in.

Explanation:

Step1: Calculate rectangular pan area

Area = length × width = $9 \times 13 = 117$ in.$^2$

Step2: Calculate area of 4-in radius pan

Area = $\pi r^2 = \pi \times 4^2 = 16\pi \approx 50.27$ in.$^2$

Step3: Calculate area of 6-in radius pan

Area = $\pi r^2 = \pi \times 6^2 = 36\pi \approx 113.10$ in.$^2$

Step4: Calculate area of 8-in radius pan

Area = $\pi r^2 = \pi \times 8^2 = 64\pi \approx 201.06$ in.$^2$

Step5: Calculate area of 10-in radius pan

Area = $\pi r^2 = \pi \times 10^2 = 100\pi \approx 314.16$ in.$^2$

Step6: Compare areas to 117 in.$^2$

Difference for 6-in pan: $|117 - 113.10| = 3.9$ in.$^2$; this is the smallest difference.

Answer:

1. The area of the 9-in. by 13-in. pan is 117 in.$^2$
2. A pan with a radius of 6 in.