Question

edwards 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: Recall the formula for the area of a circle

The area of a circle is given by \( A = \pi r^2 \), where \( r \) is the radius of the circle. We will use \( \pi \approx 3.14 \) for our calculations.

Step2: Calculate the area for each pan

• For a pan with radius \( r = 4 \) in:

\( A = 3.14 \times 4^2 = 3.14 \times 16 = 50.24 \) \( \text{in}^2 \)

• For a pan with radius \( r = 6 \) in:

\( A = 3.14 \times 6^2 = 3.14 \times 36 = 113.04 \) \( \text{in}^2 \)

• For a pan with radius \( r = 8 \) in:

\( A = 3.14 \times 8^2 = 3.14 \times 64 = 200.96 \) \( \text{in}^2 \)

• For a pan with radius \( r = 10 \) in:

\( A = 3.14 \times 10^2 = 3.14 \times 100 = 314 \) \( \text{in}^2 \)

Step3: Compare the areas with the rectangular pan's area

The area of the rectangular pan is \( 117 \) \( \text{in}^2 \). We find the absolute difference between each circular pan's area and \( 117 \):

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

The smallest difference is \( 3.96 \), which corresponds to the pan with radius \( 6 \) in.

Answer:

A pan with a radius of 6 in.