Chapter 12.4, Problem 9CE

To determine

To find: The area of the circle of intersection.

Answer to Problem 9CE

The area of the circle of intersection is $13\pi$ .

Explanation of Solution

Given information:

The given radius is $r=7$ and the distance of the plane from the centre is $h=6$ .

Calculation:

From the given figure, the triangle with the sides r, h and x is right angled triangle.

Apply Pythagoras Theorem and calculate the value of x:

  $\begin{array}{l}{r}^2=h^2+x^2\\ 7^2=6^2+x^2\\ 49=36+x^2\\ x^2=49-36\\ x^2=13\\ x=\sqrt{13}\end{array}$

Since, the circle has radius x. Therefore, area of the circle will be

  $\begin{array}{l}A=\pi x^2\\ A=\pi {\left(\sqrt{13}\right)}^2\\ A=\pi \times 13\\ A=13\pi \end{array}$

Hence,

The area of the circle of intersection is $13\pi$ .