To find the volume of a cylinder, we first need to know what a cylinder is.

A cylinder has two flat circles on top of each other, which are called bases. These bases are connected by a curved surface. The important measurements of a cylinder are:

1. Radius (r): This is how far it is from the center of the circle to the edge.
2. Height (h): This is the distance straight up between the two bases.

Step 1: Volume of a Cylinder

The volume of a cylinder is the space inside it. We can think of the volume as lots of tiny circles stacked on top of each other.

Step 2: Area of the Base

First, we need to find the area of the circle that is the base. We use this formula to do that:

$$A = \pi r^2$$

Where:

• $A$ is the area of the base.
• $r$ is the radius of the circle.
• $\pi$ (Pi) is a number that is about $3.14$.

Step 3: Stacking the Bases

Now, imagine stacking these circular bases on top of each other to make the full cylinder. If the height of the cylinder is $h$ units, we have $h$ stacks of these circular disks, each with the same area.

Step 4: Calculating the Volume

To find the total volume of the cylinder (V), we multiply the area of the base by the height:

$$V = A \times h$$

When we put in the area of the base, we get:

$$V = \pi r^2 \times h$$

So, the final formula to find the volume of a cylinder is:

$$V = \pi r^2 h$$

Application and Example

To understand this better, let’s look at an example.

Suppose we have a cylinder with a radius of 3 cm and a height of 5 cm. If we plug these numbers into the formula, we get:

$$V = \pi (3)^2 (5) = \pi (9)(5) = 45\pi \text{ cubic centimeters}$$

This is about:

$$V \approx 141.37 \text{ cubic centimeters}$$

Summary

In short, to find the volume of a cylinder, we calculate the area of its base and then multiply that by its height. The final formula is:

$$V = \pi r^2 h$$

This process helps us see how the measurements of the cylinder relate to the space inside it. Knowing this formula lets students calculate the volumes of different three-dimensional shapes easily.