Chapter 13.1, Problem 3E

To determine

To find: The area of the circle with the help of formula given on page $446$ .

Answer to Problem 3E

The area of the circle is equal to $\frac{\pi }{4}$ .

Explanation of Solution

Given information:

The circle is given below:

  

Calculation:

As shown in the figure, the radius of the circle is equal to $1$ .

The formula for the area of the circle is $A=\pi r^2$ .

Substitute 1 for r in the above formula.

  $\begin{array}{c}A=\pi {\left(1\right)}^2\\ =\pi \end{array}$

So, the area of the total circle is $\pi$ .

As shown in the figure, there is only one-fourth part of the circle. So, the area of the part of circle given in figure is one fourth of the total area.

  $A=\frac{\pi }{4}$

Therefore, the area of the circle is equal to $\frac{\pi }{4}$ .