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.
