Chapter 9.5, Problem 11PSA

a

To determine

To calculate: The Circumference of circle.

Answer to Problem 11PSA

Circumference of circle is $40.85$ units.

Explanation of Solution

Given information:

Here, we have given that in rectangle RECT, $RE\left(b\right)=5$$EC(l)=12$ .

Formula used: Diagonal of rectangle = $\sqrt{l^2+b^2}$

Circumference of circle is $2\pi r$ .

Calculation: Diagonal = $\sqrt{{(12)}^2+{(5)}^2}$

  $\begin{array}{l}\Rightarrow \sqrt{144+25}\\ \Rightarrow \sqrt{169}\\ \Rightarrow 13\end{array}$

Now, As Diagonal of the rectangle is passing through the center of circle,

  $\Rightarrow$ Diagonal of the rectangle is the diameter pf the circle.

  $\Rightarrow$ Radius = $\frac{Diameter}{2}=\frac{13}{2}=6.5$

Now, Circumference of circle = $2\pi r$

  $\begin{array}{l}\Rightarrow 2\times \frac{22}{7}\times 6.5\\ \Rightarrow \frac{286}{7}\\ \Rightarrow 40.85\end{array}$

b

To determine

To calculate: The Area of circle.

Answer to Problem 11PSA

Area of circle is $132.78{\text{ units}}^2$ .

Explanation of Solution

Given information:

Here, we have given that in rectangle RECT, $RE\left(b\right)=5$$EC(l)=12$ .

Formula used: Area of circle is $\pi r^2$ .

Calculation: Radius ( r ) = 6.5 (Proved above)

So, Area of circle = $\pi r^2$

  $\begin{array}{l}\Rightarrow \frac{22}{7}\times 6.5\times 6.5\\ \Rightarrow \frac{22}{7}\times 42.25\\ \Rightarrow \frac{929.5}{7}\\ \Rightarrow 132.78\end{array}$