To determine the volume of a cylinder, you can use the formula:

$V = \pi r^2 h$

In this formula, $V$ represents the volume of the cylinder, $r$ is the radius of the base, and $h$ is the height of the cylinder. For our example, the radius ($r$) is $3 \, \text{cm}$, and the height ($h$) is $5 \, \text{cm}$.

First, calculate the square of the radius:

$r^2 = 3^2 = 9$

This step involves multiplying the radius by itself. Next, multiply this result by the height:

$9 \times 5 = 45$

At this point, you have the product of the squared radius and the height. Now, multiply this result by $\pi$ (pi), which is approximately $3.14159$:

$V = 45 \times \pi$

To obtain a numerical approximation of the volume, substitute the value of $\pi$:

$V \approx 45 \times 3.14159 \approx 141.37 \, \text{cubic centimetres (cm}^3\text{)}$

Thus, the volume of the cylinder is approximately $141.37 \, \text{cm}^3$. This step-by-step approach clearly illustrates the process: first squaring the radius, then multiplying by the height, and finally multiplying by $\pi$. It’s important to note that the units for volume are cubic centimetres ($\text{cm}^3$) since both the radius and height are measured in centimetres.