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

The volume of the solid revolution is 508.68 in³

When a rectangle is rotated on it's side, we obtain a cylinder.

Volume of a cylinder = πr²h

• Radius, r = 9/2 = 4.5 in
• h = 8 in

Volume = 3.14 × 4.5² × 8

Volume = 508.68 in³

The volume of the solid revolution is 508.68 in³

Answer 2

V = 162π in^3

Step-by-step 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}`