The formula to calculate the height of a cone given its volume and base circumference is:
\[ h = \frac{12 \pi V}{C_{\text{Base}}^2} \]
Where:
The height of a cone is the distance between the apex of the cone and the center of its circular base.
The volume of a cone is the total quantity of three-dimensional space enclosed by the entire surface of the cone.
The base circumference of a cone is the total length of the boundary of the base circular surface of the cone.
Let's assume the following values:
Using the formula:
\[ h = \frac{12 \pi \times 520}{60^2} \approx 5.4454 \, \text{meters} \]
The height is approximately 5.4454 meters.
| Volume (cubic meters) | Base Circumference (meters) | Height (meters) |
|---|---|---|
| 500 | 55 | 6.2313 |
| 500 | 60 | 5.2360 |
| 500 | 65 | 4.4614 |
| 510 | 55 | 6.3559 |
| 510 | 60 | 5.3407 |
| 510 | 65 | 4.5507 |
| 520 | 55 | 6.4805 |
| 520 | 60 | 5.4454 |
| 520 | 65 | 4.6399 |
| 530 | 55 | 6.6051 |
| 530 | 60 | 5.5501 |
| 530 | 65 | 4.7291 |
| 540 | 55 | 6.7298 |
| 540 | 60 | 5.6549 |
| 540 | 65 | 4.8183 |