Question

1b. if the polygon shown below is rotated about the x - axis, what will be the height of the 3 - dimensional figure that is created?

Explanation:

Step1: Identify the shape after rotation

When the rectangle (polygon) is rotated about the x - axis, it forms a cylinder.

Step2: Determine the height of the cylinder

The height of the cylinder is the length of the side parallel to the x - axis.
The x - coordinate of point A is \(x=-4\) and the x - coordinate of point D is \(x = 4\).
Using the distance formula for two points on the x - axis \(d=\vert x_2 - x_1\vert\), here \(x_1=-4\) and \(x_2 = 4\).
\(d=\vert4-(-4)\vert=\vert4 + 4\vert=8\)

Answer:

\(8\)