The formula for the volume of a disk, which in this context refers to a three-dimensional shape akin to a cylinder, is Pi * r^2 * h.
Understanding the Formula for Disk Volume
When discussing the "formula for a disk," particularly when a height (h) is involved, it typically refers to the calculation of its volume. A disk in this sense is a circular prism or cylinder, a 3D object with a circular base and a certain height.
Key Components of the Formula
The formula V = Pi * r^2 * h breaks down into specific components:
| Component | Description |
|---|---|
| Pi (π) | This is a fundamental mathematical constant, approximately equal to 3.14159. It represents the ratio of a circle's circumference to its diameter. As the reference states, Pi is, well, Pi. |
| r | Stands for the radius of the disk's circular base. The radius is the distance from the center of the circle to any point on its edge. |
| h | Represents the height of the disk. This is the perpendicular distance between the two circular faces of the disk. |
The term r^2 (r squared) means the radius multiplied by itself (r * r). The Pi * r^2 part of the formula calculates the area of the circular base, and then multiplying by h extends that area through the height to determine the total volume.
Practical Example: Calculating Disk Volume
To illustrate how to use the formula, let's consider an example provided in the reference, where we are trying to find the volume of a disk with specific dimensions:
- Radius (r): 12 units
- Height (h): 3.06 units (The reference provided "3.06-Apr-2017" for height; for calculation purposes, we use the numerical value of 3.06)
Here's how to calculate the volume step-by-step:
- Identify the values:
r = 12h = 3.06Pi ≈ 3.14159
- Calculate r squared (r^2):
r^2 = 12 * 12 = 144
- Multiply Pi by r^2:
Pi * r^2 = 3.14159 * 144 ≈ 452.389
- Multiply the result by the height (h):
Volume = (Pi * r^2) * h = 452.389 * 3.06 ≈ 1384.33
Therefore, the volume of a disk with a radius of 12 and a height of 3.06 is approximately 1384.33 cubic units.
