Question

height and radius #1
the rectangle is rotated around the x - axis
what is the radius of the cylinder?
check your work: keep trying.
youve tried 1 times.
what is the height of the cylinder?
check your work: keep trying.
youve tried 0 times.

Explanation:

Step1: Determine the radius

When a rectangle is rotated around the x - axis, the radius of the resulting cylinder is the distance from the x - axis to the side of the rectangle. Looking at the graph, the vertical distance from the x - axis (y = 0) to the top (or bottom) of the rectangle is 6 units. So the radius \(r = 6\).

Step2: Determine the height

The height of the cylinder is the length along the x - axis. The rectangle extends from \(x=- 5\) to \(x = 5\). Using the distance formula \(d=\vert x_2 - x_1\vert\), where \(x_1=-5\) and \(x_2 = 5\). Then \(h=\vert5-(-5)\vert=\vert5 + 5\vert=10\).

Answer:

Radius: \(6\)
Height: \(10\)