Question

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

Explanation:

Step1: Understand the rotation concept

When a figure is rotated about the x - axis, the distance from the x - axis to the figure (perpendicular distance) gives the radius of the resulting 3 - D figure.

Step2: Calculate the perpendicular distance

The y - coordinate of points \(A\) and \(D\) is \(0\), and the y - coordinate of points \(B\) and \(C\) is \(- 2\). The perpendicular distance from the polygon to the x - axis is the absolute value of the non - zero y - coordinate. Using the formula for the distance \(d=\vert y\vert\), where \(y\) is the y - coordinate of the points of the polygon (excluding those on the x - axis). Here, \(y=-2\), and \(\vert - 2\vert=2\).

Answer:

\(2\)