Question

7.3 covering a circle
here is a square whose side length is the same as the radius of the circle.
how many of these squares do you think it would take to cover the circle exactly?

Explanation:

Step1: Recall area formulas

The area of a circle is \(A_{circle}=\pi r^{2}\), and the area of a square with side length \(r\) is \(A_{square}=r\times r = r^{2}\).

Step2: Calculate the ratio

We want to find out how many squares (\(n\)) are needed to cover the circle. So we use the formula \(n=\frac{A_{circle}}{A_{square}}\). Substituting the area formulas, we get \(n = \frac{\pi r^{2}}{r^{2}}\). Since \(r
eq0\) (as it is a radius of a non - degenerate circle), the \(r^{2}\) terms cancel out, and \(n=\pi\approx3.14\).

Answer:

It would take approximately \(3.14\) (or \(\pi\)) such squares to cover the circle exactly.