Chapter 5.7, Problem 21PSB

To determine

Tofind: area of the given circle to the nearest hundredth.

Answer to Problem 21PSB

The area of the given circle to the nearest hundredth is, $A\approx 29.62{\text{ untis}}^2$ .

Explanation of Solution

Given information:

In the circle $\odot P$ :

Centre $\left(P\right)=\left(5,3.07\right)$

Circle touches $x-axis$ at $Q\left(5,0\right)$

Formula used:

Area of the circle with radius $\left(r\right)$ is, $A=\pi r^2{\text{ units}}^2$

Calculation:

Given centre of the circle is $P\left(5,3.07\right)$

Radius of the circle is, $r=PQ=\sqrt{{\left(5-5\right)}^2+{\left(0-3.07\right)}^2}=3.07\text{ units}$

Area of the circle is,

  $\begin{array}{c}\left(A\right)=\pi r^2\\ \approx \frac{22}{7}\times {\left(3.07\right)}^2\\ \approx \frac{22}{7}\times 9.4249\\ \approx \frac{207.3478}{7}\\ \approx 29.62111429\end{array}$

Therefore, the area of the given circle to the nearest hundredth is, $A\approx 29.62{\text{ untis}}^2$ .