Given the word problem, we can deduce the following information:
1. The diameter of the circle is 3 meters.
2. The side length of the square is 3 meters.
To determine the difference in area between a circle and a square, we note first the formulas of a circle with a diameter d and the area of a square with side length d:
[tex]A_{circle}=\frac{\pi d^2}{4}[/tex]
where:
d=diameter
[tex]\text{A}_{square}=d^2[/tex]
where:
d=side length
The figures are shown below:
Based on this, the difference of areas would be:
[tex]\begin{gathered} A_{square}-A_{circle}=d^2-\frac{\pi d^2}{4} \\ \end{gathered}[/tex]
Next, we plug in d=3:
[tex]\begin{gathered} A_{square}-A_{circle}=d^2-\frac{\pi d^2}{4} \\ =(3)^2-\frac{\pi(3)^2}{4} \\ =9-\frac{9\pi}{4} \end{gathered}[/tex]
Therefore, the difference in areas is:
[tex]9-\frac{9\pi}{4}[/tex]
