Chapter E, Problem 12.9EX

To determine

To find: The area of the circle of intersection.

Answer to Problem 12.9EX

The area of the circle of intersection $=12\pi {\text{ cm}}^2$ .

Explanation of Solution

Given information: A plane passes $2\text{ cm}$ from the center of a sphere with radius $\text{4 cm}$ .

Calculation:

A plane passes $2\text{ cm}$ from the center of a sphere with radius $\text{4 cm}$ .

Radius of the circle of intersection $=\sqrt{4^2-2^2}$

Radius of the circle of intersection $=\sqrt{12}$ cm

The area of the circle of intersection $=\pi r^2$

The area of the circle of intersection $=12\pi {\text{ cm}}^2$ .