Chapter 3, Problem 10RP

To determine

To calculate: Area and circumference of circle

Answer to Problem 10RP

Area of circle is $310$ square units and circumference is $60$ units.

Explanation of Solution

Given information : Here, we have given a circle with center O

Formula used : Distance formula = $\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$ , Area of circle = $\pi r^2$ and circumference of circle = $2\pi r$

Calculation: Here, radius will be half of the distance between $(2,4)$ and $(12,4)$

Distance (d) =

  $\begin{array}{l}=\sqrt{{(12-2)}^2+{(4-4)}^2}\\ \Rightarrow \sqrt{{(10)}^2+{(0)}^2}\\ \Rightarrow \sqrt{100}\\ \Rightarrow \pm 10\end{array}$

As, distance cannot be negative,

  $\therefore$ d = $10$

Now, radius = $\frac{10}{2}=5$

So, area = $\pi r^2$

  $\begin{array}{l}=\frac{22}{7}\times {(}^{10}\\ \Rightarrow \frac{22}{7}\times 100\\ \Rightarrow 314.28\end{array}$

Nearest tenth = $310$ square units

Now, circumference = $2\pi r$

  $\begin{array}{l}=2\times \frac{22}{7}\times 10\\ \Rightarrow 62.85\end{array}$

Nearest tenth = $60$ units