What is the volume of a cylinder if the diameter is 1.5 inches and the height is 4 inches?

To find the volume of a cylinder, the formula used is:

[ V = \pi r^2 h ]

where ( V ) is the volume, ( r ) is the radius, and ( h ) is the height of the cylinder.

In this case, the diameter of the cylinder is given as 1.5 inches; therefore, the radius ( r ) is half of the diameter:

[ r = \frac{1.5}{2} = 0.75 \text{ inches} ]

The height ( h ) is given as 4 inches.

Substituting these values into the volume formula:

[ V = \pi (0.75)^2 (4) ]

First, calculate the area of the base (( r^2 )):

[ (0.75)^2 = 0.5625 ]

Then, multiply that by the height:

[ 0.5625 \times 4 = 2.25 ]

Now, multiply by ( \pi ):

[ V = \pi \times 2.25 \approx 3.14159 \times 2.25 \approx 7.06858 ]

Thus,