The formula to calculate the base area of a cone given its lateral surface area and slant height is:
\[ A_{\text{Base}} = \pi \left(\frac{LSA}{\pi \cdot h_{\text{Slant}}}\right)^2 \]
Where:
The base area of a cone is the total quantity of plane enclosed on the base circular surface of the cone.
The lateral surface area of a cone is the total quantity of plane enclosed on the lateral curved surface of the cone.
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 of the cone.
Let's assume the following values:
Using the formula:
\[ A_{\text{Base}} = \pi \left(\frac{350}{\pi \cdot 11}\right)^2 \approx 322.2559 \, \text{square meters} \]
The base area is approximately 322.2559 square meters.
| Lateral Surface Area (square meters) | Slant Height (meters) | Base Area (square meters) |
|---|---|---|
| 300 | 10 | 286.4789 |
| 300 | 11 | 236.7594 |
| 300 | 12 | 198.9437 |
| 310 | 10 | 305.8958 |
| 310 | 11 | 252.8064 |
| 310 | 12 | 212.4276 |
| 320 | 10 | 325.9493 |
| 320 | 11 | 269.3796 |
| 320 | 12 | 226.3537 |
| 330 | 10 | 346.6395 |
| 330 | 11 | 286.4789 |
| 330 | 12 | 240.7219 |
| 340 | 10 | 367.9662 |
| 340 | 11 | 304.1043 |
| 340 | 12 | 255.5321 |
| 350 | 10 | 389.9296 |
| 350 | 11 | 322.2559 |
| 350 | 12 | 270.7845 |
| 360 | 10 | 412.5296 |
| 360 | 11 | 340.9336 |
| 360 | 12 | 286.4789 |
| 370 | 10 | 435.7662 |
| 370 | 11 | 360.1374 |
| 370 | 12 | 302.6154 |
| 380 | 10 | 459.6395 |
| 380 | 11 | 379.8673 |
| 380 | 12 | 319.1941 |
| 390 | 10 | 484.1493 |
| 390 | 11 | 400.1234 |
| 390 | 12 | 336.2148 |
| 400 | 10 | 509.2958 |
| 400 | 11 | 420.9056 |
| 400 | 12 | 353.6777 |