Question

A rectangle has dimensions of 9 in. by 8 in. Find the exact volume (in cubic inches) of the solid of revolution formed when the rectangle is rotated about its 8 in. side.Incorrect: Your answer is incorrect.in3

Answer 1

V = 162π in^3

Explanation:

Since rotation a rectangle on its side result to a cylinder.

We'll use the formula for the volume of a cylinder with 8in being the height (since the rectangle is rotated around that side) and 9 in as the diameter.

Data:

Radius : r = diameter / 2 = 9/2 = 4.5 in

Height : h = 8 in

Formula:

$V=\pi *r^2*h$

Solution:

$\begin{gathered} V=\pi *4.5^2*8 \\ V=162\pi\text{ }in^3 \end{gathered}$