Chapter 11.5, Problem 35WE

To determine

To Construct: A circle whose area is equal to the sum of these two circles.

Answer to Problem 35WE

The new circle is of the radius $5cm$ .

Explanation of Solution

Given: Draw any circle $O$ and any circle $P$

Let the radius of the circle $O$ is $3cm$ .

  

The area of circle

  $\begin{array}{l}{A}_o=\pi r^2\\ $ A_o=\pi {(3)}^2$A_o=9\pi \end{array}$

Similarly

Let the radius of the circle $P$ is $4cm$ .

  

The area of circle

  $\begin{array}{l}{A}_p=\pi r^2\\ $ A_o=\pi {(4)}^2$A_p=16\pi \end{array}$

Sum of the area of the circles.

  $\begin{array}{l}A=A_o+A_p\\ A=9\pi +16\pi \\ A=25\pi \end{array}$

i.e.

The area of new circle is $A=25\pi$

We have to find the radius of new circle.

Thus

  $\begin{array}{l}A=\pi r^2\\ 25\pi =\pi r^2\\ r^2=25\\ r=5cm\end{array}$

Thus