Question

edwards grandmother used to make him pannukakku when he was little. he wants to surprise 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 in²
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 area of rectangular pan

The area of a rectangle is $A = l\times w$. Given $l = 13$ in and $w=9$ in, so $A_{rect}=13\times9 = 117$ in².

Step2: Calculate areas of round pans

The area of a circle is $A=\pi r^{2}$.
For a pan with $r = 4$ in, $A_1=\pi\times4^{2}=16\pi\approx16\times 3.14 = 50.24$ in².
For a pan with $r = 6$ in, $A_2=\pi\times6^{2}=36\pi\approx36\times3.14 = 113.04$ in².
For a pan with $r = 8$ in, $A_3=\pi\times8^{2}=64\pi\approx64\times3.14 = 200.96$ in².
For a pan with $r = 10$ in, $A_4=\pi\times10^{2}=100\pi\approx100\times3.14 = 314$ in².

Step3: Find the closest - area pan

Compare the differences:
$|117 - 50.24|=66.76$, $|117 - 113.04| = 3.96$, $|117 - 200.96|=83.96$, $|117 - 314| = 197$.
The smallest difference is $3.96$ which corresponds to the pan with $r = 6$ in.

Answer:

A pan with a radius of 6 in.