Question

Calculate the area of the circle, using the formula given on page 446.

Compare this result with your computer approximations.

Short answer

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

Step-by-step solution

Step-1 – Given

The given circle is:

Step-2 – To determine

We have to find the area of the circle with the help of formula given on page 446.

Step-3 – Calculation 

From the figure, the radius of the circle is 1.

We know that the formula for the area of the circle is:$A=\pi r^2$.

Then we substitute 1 for r in the formula.

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

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

From the figure, only one-fourth part of the circle is given. It means, the required area is one fourth of the total area.

$A=\frac{\pi }{4}$

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