Chapter 12.4, Problem 14WE

To determine

To find: The area of the circle formed

Answer to Problem 14WE

The area of the circle formed is $15\pi {\text{ cm}}^2$ .

Explanation of Solution

Given information:

The plane passes 7 cm from the center of a sphere with radius 8 cm.

Calculation:

Since, the plane passes 2 cm form the center of the sphere.

  

From the above figure, the triangle ABC is right angled triangle.

Apply Pythagoras Theorem and calculate the value of x:

  $\begin{array}{l}{r}^2=h^2+x^2\\ 8^2=7^2+x^2\\ 64=49+x^2\\ x^2=64-49\\ x^2=15\\ x=\sqrt{15}\end{array}$

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

  $\begin{array}{l}A=\pi x^2\\ A=\pi {\left(\sqrt{15}\right)}^2\\ A=\pi \times 15\\ A=15\pi {\text{ cm}}^2\end{array}$

Hence,

The area of the circle formed is $15\pi {\text{ cm}}^2$ .