Chapter 12.4, Problem 13WE

To determine

To find: The area of the circle formed

Answer to Problem 13WE

The area of the circle formed is $21\pi {\text{ cm}}^2$ .

Explanation of Solution

Given information:

The plane passes 2 cm from the center of a sphere with radius 5 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:

  $\begin{array}{l}{r}^2=h^2+x^2\\ 5^2=2^2+x^2\\ 25=4+x^2\\ x^2=25-4\\ x^2=21\\ x=\sqrt{21}\end{array}$

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

  $\begin{array}{l}A=\pi x^2\\ A=\pi {\left(\sqrt{21}\right)}^2\\ A=\pi \times 21\\ A=21\pi {\text{ cm}}^2\end{array}$

Hence,

The area of the circle formed is $21\pi {\text{ cm}}^2$ .