If the segment of the line ` y=-2x+2` that lies in quadrant I is rotated about the y-axis , a cone is formed . What is the volume of the cone ?

Explanation

To find the volume of the cone formed by rotating the segment of the line \( y = -2x + 2 \) that lies in the first quadrant about the y-axis, we can follow these steps:

### Step 1: Find the points where the line intersects the axes
To determine the segment of the line in the first quadrant, we need to find the x-intercept and y-intercept of the line.

1. **Y-intercept**: Set \( x = 0 \):
\[
y = -2(0) + 2 = 2
...