How To Find The Volume Of A Right Cylinder

Calculating the volume of a right cylinder is a common geometric operation that involves understanding the relationship between its radius and height. This article will guide you through the steps to find the volume of a right cylinder using the appropriate formula. We'll explain the formula, show an example, and provide the final value.

Understanding the Volume Formula

The volume ($V$) of a right cylinder can be calculated using the following algebraic formula:

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

Where:

- $r$ is the radius of the cylinder's base.

- $h$ is the height of the cylinder.

- $\pi$ (Pi) is a constant approximately equal to 3.14159.

Explanation of the Formula

- The term $r^2$ represents the area of the cylinder's circular base.

- Multiplying by $\pi$ gives the exact area of the base.

- Multiplying by $h$ extends this base area through the height of the cylinder, resulting in the total volume.

Step-by-Step Calculation

Let's calculate the volume of a right cylinder with given dimensions.

Example: Calculating the Volume of a Right Cylinder

1. Identify the given values:

  - Radius of the cylinder's base ($r$) = 3 units

  - Height of the cylinder ($h$) = 5 units

2. Substitute the values into the volume formula:

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

$$V=\pi \cdot 3^2\cdot 5$$

3. Calculate the area of the base:

$$3^2=9$$

$$\pi \cdot 9=9\pi$$

4. Calculate the volume:

$$9\pi \cdot 5=45\pi$$

5. Use the value of $\pi \approx 3.14159$ to get the final volume:

$$45\pi \approx 45\cdot 3.14159=141.37155$$

Final Value

The volume of a right cylinder with a radius of 3 units and a height of 5 units is approximately 141.37 cubic units.

Summary

By using the formula $V=\pi \cdot r^2\cdot h$, you can easily calculate the volume of a right cylinder. This fundamental geometric concept is essential for various academic and practical applications.