Calculating the volume of an oblique cylinder is a straightforward task if you understand the relationship between its radius, height, and the constant \( \pi \). This article will guide you through the steps to find the volume 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 an oblique cylinder can be calculated using the same formula as for a right cylinder:
\[ V = \pi \cdot r^2 \cdot h \]
Where:
- \( r \) is the radius of the base of the cylinder.
- \( h \) is the perpendicular 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 circular base.
- Multiplying by \( \pi \) gives the exact area of the circular base.
- Multiplying by \( h \) (the perpendicular height) 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 an oblique cylinder with given dimensions.
Example: Calculating the Volume of an Oblique Cylinder
1. Identify the given values:
- Radius of the base (\( r \)) = 4 units
- Perpendicular height (\( h \)) = 10 units
2. Substitute the values into the volume formula:
\[ V = \pi \cdot r^2 \cdot h \]
\[ V = \pi \cdot 4^2 \cdot 10 \]
3. Calculate the area of the base:
\[ 4^2 = 16 \]
4. Multiply the base area by the height:
\[ 16 \cdot 10 = 160 \]
5. Calculate the volume:
\[ V = \pi \cdot 160 \]
6. Use the value of \( \pi \approx 3.14159 \) to get the final volume:
\[ 160\pi \approx 160 \cdot 3.14159 = 502.65482 \]
Final Value
The volume of an oblique cylinder with a radius of 4 units and a height of 10 units is approximately 502.65 cubic units.
