Question

now it’s time to practice on your own
what is the volume of the object generated by rotating the rectangle about the vertical axis?
4 in.
8 in.
axis
express your answer in terms of \\(\pi\\).
enter your answer in the box.
volume = \\(\square\\) in\\(^3\\)

Explanation:

Step1: Identify the shape formed

When a rectangle is rotated about a vertical axis, it forms a cylinder. The radius of the cylinder ($r$) is the horizontal side of the rectangle, and the height ($h$) is the vertical side. From the diagram, $r = 8$ in and $h = 4$ in.

Step2: Use the volume formula for a cylinder

The formula for the volume of a cylinder is $V=\pi r^{2}h$. Substitute $r = 8$ and $h = 4$ into the formula:
$V=\pi\times(8)^{2}\times4$
$V=\pi\times64\times4$
$V = 256\pi$

Answer:

$256\pi$