**Introduction**

In this lesson, you will find the volume of a rectangular object. To do this, you must find the area of the base and multiply it by the height. You can find the volume of a cylinder in the same way.

This video illustrates the lesson material below. Watching the video is optional.

**Volume of a Right Circular Cylinder: \(V = \pi r^2h\)**

When you find the volume of a rectangular object, you find the area of the base and multiply it by the height. Do the same thing to find the volume of a cylinder only this time the base is a circle. Find the area of the base \( \pi r^2 \) and multiply that by the height of the cylinder.

Here is some vocabulary to help with this lesson.

**Radius (r):**The distance from the center of the circle to the edge or half of the diameter.**Height (h):**The distance from the bottom to the top of a shape or object.**Right Angle**: This is the same thing as perpendicular, two lines come together at 90 degrees like the corner of a rectangle.**Right Circular Cylinder**: A shape like a tube, the ends (or base) form a circle and the sides are perpendicular to the base. The circular bases will always be parallel for Right Circular Cylinders.

Figure 1

**Example 1**

The radius of the circular base of a cylinder is 1.5 inches and the height is 5 inches. What is the volume of the cylinder?

Figure 2

\begin{align*}V&=\pi r^2h &\color{red}\small\text{Formula for volume of a cylinder}\\\\V&=\pi(1.5in)^2(5in) &\color{red}\small\text{Substitute given terms}\\\\V&=\pi(2.25in^2)(5in) &\color{red}\small\text{Solve exponents}\\\\

V&=\pi11.25in^3 &\color{red}\small\text{Multiply}\\\\V&=(3.14)11.25in^3 &\color{red}\small\text{Substitute \(\pi\)}\\\\V&= 35.34in^3 &\color{red}\small\text{Multiplication property}\\\end{align*}

**Example 2**

The radius of the circular base of a cylinder is 2.4 inches and the height is 6 inches. What is the volume of the cylinder? Round to the nearest tenth.

\begin{align*}V&=\pi r^2h &\color{red}\small\text{Formula for volume of a cylinder}\\\\V&=\pi(2.4in)^2(6in) &\color{red}\small\text{Substitute given terms}\\\\V&=\pi(5.76in^2)(6in) &\color{red}\small\text{Solve exponents}\\\\V&=\pi34.56in^3 &\color{red}\small\text{Multiply}\\\\V&=(3.14)34.56in^3 &\color{red}\small\text{Substitute \(\pi\)}\\\\V&= 108.5in^3 &\color{red}\small\text{Multiplication property}\\\end{align*}

**Things to Remember**

- To find the volume of a cylinder, determine the area of the base and multiply it by the height: \(V = \pi r^2h\).

### Practice Problems

- A can of food is a right circular cylinder with a radius of 5 cm and a height of 16 cm. Find the volume of the can. Round your answer to the nearest tenth. (Solution
- A paint can is a right circular cylinder with a radius of 3.5 inches and a height of 7.5 inches. Find the volume of the paint can. Round your answer to the nearest hundredth. (Solution
- A water tower is used to pressurize the water supply for the distribution of water in the surrounding area. A particular water tower is in the shape of a right circular cylinder with a radius of 4.25 meters and a height of 7.5 meters. Find the volume of the water tower. Round your answer to the nearest whole number. (Solution
- A 55-gallon drum is in the shape of a right circular cylinder with a diameter of 22.5 inches and a height of 33.5 inches. First, find the radius of the drum and then use the radius to find the volume of the drum. Round your answer to the nearest hundredth. (Video Solution
- A support column on a building is a right circular cylinder. It has a radius of 1.5 feet and a height of 16 feet. Find the volume of the column. Round your answer to the nearest whole number. (Solution
- A triple-A battery is a right circular cylinder with a radius of 5.25 mm and a height of 44.5 mm. Find the volume of the battery. Round to the nearest tenth. (Video Solution

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