Chapter 12, Problem 8CUR

To determine

To check: Whether the given statement is true or false.

Answer to Problem 8CUR

The given statement is True.

Explanation of Solution

Given information: The statement is “When a square is circumscribed about a circle, the ratio of the areas is $4:\pi$ ”.

According to the given statement a circle is inside a square. So, the diameter of the circle and side of the square are equal.

Consider side of a square as $s$ and radius of the circle as $r$ . So,

  $s=2r$

The formula for area of the square is:

  $\begin{array}{c}{A}_1=s^2\\ ={\left(2r\right)}^2\\ =4r^2\end{array}$

The formula for area of the circle is:

  $A_2=\pi {\text{r}}^2$

The ratio of the areas is:

  $\begin{array}{c}\frac{A_1}{A_2}=\frac{4r^2}{\pi r^2}\\ =\frac{4}{\pi }\end{array}$

Therefore, the given statement is True.