Question

what is the difference in area between a circle with a diameter of 3 meters and a square with a side length of 3 meters? Write Your Answer In Terms Of pi.

Answer 1

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:

`A_(circle)=(\pi d^2)/(4)`

where:

d=diameter

`\text{A}_(square)=d^2`

where:

d=side length

The figures are shown below:

Based on this, the difference of areas would be:

`\begin{gathered} A_(square)-A_(circle)=d^2-(\pi d^2)/(4) \\ \end{gathered}`

Next, we plug in d=3:

`\begin{gathered} A_(square)-A_(circle)=d^2-(\pi d^2)/(4) \\ =(3)^2-(\pi(3)^2)/(4) \\ =9-(9\pi)/(4) \end{gathered}`

Therefore, the difference in areas is:

`9-(9\pi)/(4)`