Question

2c. if the polygon shown below is rotated about the y - axis, what will be the radius of the 3 - dimensional figure that is created?

Explanation:

Step1: Understand the rotation concept

When a polygon (here a right - triangle \(ABC\) with \(A=(0,0)\), \(B=(0,5)\), \(C=(3,0)\)) is rotated about the \(y\) - axis, the radius of the resulting 3 - dimensional figure (a cone) is the distance of the point (not on the axis of rotation) from the \(y\) - axis.
For a point \((x,y)\) in the coordinate plane, the distance from the \(y\) - axis is given by \(|x|\).

Step2: Identify the relevant point

The vertices of the triangle are \(A=(0,0)\), \(B=(0,5)\) (both on the \(y\) - axis, so their distance from the \(y\) - axis is \(0\)) and \(C=(3,0)\).
The \(x\) - coordinate of point \(C\) is \(x = 3\). The distance of point \(C\) from the \(y\) - axis is \(r=|x|\).

Answer:

\(3\)