Question

fill in the blank 1 point
each small square represents 1 square centimeter.
a. sketch and label the solid formed by rotating this
two - dimensional figure around the horizontal axis
shown.
b. what is the volume of the solid? leave your answer in terms of pi.
type your answer...

Explanation:

Step1: Determine the radius and height of the cylinder

When the two - dimensional figure (a rectangle) is rotated around the horizontal axis, it forms a cylinder. Each small square represents 1 square centimeter, so the side length of each square is 1 centimeter. The height \(h\) of the cylinder is 3 centimeters and the radius \(r\) is 2 centimeters.

Step2: Use the formula for the volume of a cylinder

The formula for the volume of a cylinder is \(V=\pi r^{2}h\). Substitute \(r = 2\) and \(h=3\) into the formula: \(V=\pi\times(2)^{2}\times3\).

Step3: Calculate the volume

First, calculate \((2)^{2}=4\). Then, \(V=\pi\times4\times3 = 12\pi\)

Answer:

\(12\pi\)