Welcome to Calculate Volume of Cylinders! In the previous lessons, you mastered the volume of rectangular prisms and discovered the universal formula $V = B \times h$. Now, you will apply that same "base area times height" logic to a curved surface: the cylinder.

This third lesson focuses on measuring cylindrical volume by using what you know about circular areas. You will learn how to adapt your volume formula for objects like soup cans, water pipes, and fuel tanks. By the end, you will be able to:

• Apply the formula $V = \pi r^2 h$ to calculate the volume of any cylinder.
• Convert a diameter into a radius to avoid common calculation errors.
• Manage the decimal values of $\pi$ to provide both exact and rounded measurements.

As you may recall from the previous lesson, any solid built from identical layers stacked to a uniform height follows the formula $V = B \times h$. You used rectangular bases last time, but the shape of the base does not always have to be a rectangle.

A cylinder is a solid whose base is a circle instead of a rectangle. Imagine stacking hundreds of thin circular discs, like a tall roll of coins. Each disc has the same circular area, and the total number of discs determines the height. The same "base area times height" logic applies perfectly, so all you need is a way to find the area of that circular base.

Before you write the cylinder volume formula, let's do a quick refresher. As you may recall from an earlier course, the area of a circle is:

Here, $r$ is the radius (the distance from the center of the circle to its edge) and $\pi$ is approximately $3.14$. For example, a circle with a radius of cm has an area of .

Now let's combine what you know. A cylinder's base is a circle with area $B = \pi r^2$, and its height is $h$. Plugging this into the general volume formula gives you:

Sometimes a problem provides the diameter rather than the radius. Since the radius is half the diameter, you simply add one small step at the beginning.

Example: A soup can has a diameter of $7$ cm and a height of $11$ cm. What is its volume?

1. Find the radius: $r = \frac{d}{2} = \frac{7}{2} = 3.5 \ \text{cm}$

In this lesson, you extended the $V = B \times h$ formula from rectangular prisms to cylinders by recognizing that a cylinder's base is a circle with area $\pi r^2$. The complete cylinder volume formula is $V = \pi r^2 \times h$. When given a diameter, you divide by to find the radius first.