Introduction

Calculating the volume of a solid cylinder is a fundamental concept in geometry and mathematics. A cylinder is a three-dimensional shape with a circular base and straight sides. In this article, we will explore the formula for finding the volume of a solid cylinder when the height is given. Specifically, we will focus on a cylinder with a height of 2.4 units.

Understanding the Formula

The formula for calculating the volume of a cylinder is:

[ V = \pi r^2 h ]

Where:
– ( V ) = Volume of the cylinder
– ( \pi ) ≈ 3.14159
– ( r ) = Radius of the circular base
– ( h ) = Height of the cylinder

When the height of the cylinder is known, finding the volume involves multiplying the area of the circular base by the height of the cylinder.

Given:
– Height (h) = 2.4 units

Steps to Calculate the Volume

Step 1: Find the Area of the Base

The base of a cylinder is a circle, and the formula to find the area of a circle is:

[ A = \pi r^2 ]

Step 2: Substitute the Known Values

Substitute the given height into the formula for the volume of a cylinder:

[ V = \pi r^2 (2.4) ]

Step 3: Determine the Radius

To find the value of the radius (( r )), you may need additional information. If the radius is given, you can directly substitute the value into the formula. If the radius is not given, and only the height is provided, you may need to make assumptions or use other methods to calculate the radius.

Step 4: Calculate the Volume

Once you have the radius value, plug it back into the formula to find the volume.

Calculations Example

Let’s consider an example where the radius of the cylinder is given as 3 units. Now, we can calculate the volume using the formula:

[ A = \pi (3)^2 ]
[ A = 9\pi ]

Now, substitute the area into the volume formula:

[ V = 9\pi \times 2.4 ]
[ V = 21.6\pi ]
[ V \approx 67.947 \text{ cubic units (rounded to three decimal places)} ]

Therefore, the volume of a cylinder with a height of 2.4 units and a radius of 3 units is approximately 67.947 cubic units.

Conclusion

Calculating the volume of a cylinder is essential in various fields, including mathematics, engineering, and construction. Understanding the formula and steps involved in finding the volume when the height is given can be useful in solving practical problems related to cylinders. By following the steps outlined in this article, you can accurately determine the volume of a solid cylinder with a specified height.