The formula to calculate the Height of a Cone given its slant height and base radius is:
\[ \text{Height} = \sqrt{\text{Slant Height}^2 - \text{Base Radius}^2} \]
The Height of a Cone is the distance between the apex of the cone to the center of its circular base. The Slant Height of a Cone is the length of the line segment joining the apex of the cone to any point on the circumference of the circular base. The Base Radius of a Cone is the distance between the center and any point on the circumference of the base circular surface of the cone.
Let's assume the following values:
Using the formula:
\[ \text{Height} = \sqrt{11^2 - 10^2} \approx 4.5826 \, \text{meters} \]
The Height is approximately 4.5826 meters.
| Slant Height (meters) | Base Radius (meters) | Height (meters) |
|---|---|---|
| 10 | 9 | 4.358898943540674 |
| 10 | 9.5 | 3.122498999199199 |
| 10 | 10 | 0.000000000000000 |
| 10 | 10.5 | nan |
| 10 | 11 | nan |
| 10.5 | 9 | 5.408326913195984 |
| 10.5 | 9.5 | 4.472135954999580 |
| 10.5 | 10 | 3.201562118716424 |
| 10.5 | 10.5 | 0.000000000000000 |
| 10.5 | 11 | nan |
| 11 | 9 | 6.324555320336759 |
| 11 | 9.5 | 5.545268253204709 |
| 11 | 10 | 4.582575694955840 |
| 11 | 10.5 | 3.278719262151000 |
| 11 | 11 | 0.000000000000000 |
| 11.5 | 9 | 7.158910531638177 |
| 11.5 | 9.5 | 6.480740698407860 |
| 11.5 | 10 | 5.678908345800274 |
| 11.5 | 10.5 | 4.690415759823430 |
| 11.5 | 11 | 3.354101966249685 |
| 12 | 9 | 7.937253933193772 |
| 12 | 9.5 | 7.331439149307590 |
| 12 | 10 | 6.633249580710800 |
| 12 | 10.5 | 5.809475019311125 |
| 12 | 11 | 4.795831523312719 |