Journeyman Plumber Practice Exam

To find the volume of a cylinder, the essential formula is based on the area of its circular base and its height (or length). The volume \( V \) is calculated with the formula:

\[ V = \text{Base Area} \times \text{Height} \]

For a cylinder, the base is a circle, and the area \( A \) of a circle is given by:

\[ A = \pi r^2 \]

Where \( r \) is the radius. The radius is half of the diameter \( D \):

\[ r = \frac{D}{2} \]

Therefore, substituting this into the area formula, we convert it to involve diameter:

\[ A = \pi \left(\frac{D}{2}\right)^2 \]

This can be simplified to:

\[ A = \frac{\pi D^2}{4} \]

Now, substituting the base area into the volume formula gives:

\[ V = \frac{\pi D^2}{4} \times \text{Height} \]

In this case, the height corresponds to the length of the cylinder. To express this in terms of the entire formula to compute the volume using diameter and length:

\[ V =