Question

edwards grandmother used to make him pannukakku when he was little. he wants to surprise he 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. a = πr²

Explanation:

Step1: Calculate the area of each round pan

The formula for the area of a circle is \(A = \pi r^{2}\).

• For \(r = 4\) in:

\(A=\pi\times4^{2}=16\pi\approx16\times3.14 = 50.24\) in\(^{2}\)

• For \(r = 6\) in:

\(A=\pi\times6^{2}=36\pi\approx36\times3.14=113.04\) in\(^{2}\)

• For \(r = 8\) in:

\(A=\pi\times8^{2}=64\pi\approx64\times3.14 = 200.96\) in\(^{2}\)

• For \(r = 10\) in:

\(A=\pi\times10^{2}=100\pi\approx100\times3.14=314\) in\(^{2}\)

Step2: Find the difference between the area of the rectangular pan and each round pan

The area of the rectangular pan is \(117\) in\(^{2}\).

• For \(r = 4\) in: \(|117 - 50.24|=66.76\)
• For \(r = 6\) in: \(|117-113.04| = 3.96\)
• For \(r = 8\) in: \(|117 - 200.96|=83.96\)
• For \(r = 10\) in: \(|117-314|=197\)

Answer:

B. A pan with a radius of 6 in.