The formula to calculate the Slant Height of a Right Square Pyramid given the Volume is:
\[ h_{slant} = \sqrt{\frac{le(Base)^2}{4} + \left(\frac{3V}{le(Base)^2}\right)^2} \]
The Slant Height of a Right Square Pyramid is the length measured along the lateral face from the base to the apex along the center of the face. The Edge Length of the Base is the length of the straight line connecting any two adjacent vertices of the base. The Volume is the total quantity of three-dimensional space enclosed by the surface of the pyramid.
Let's assume the following values:
Using the formula:
\[ h_{slant} = \sqrt{\frac{10^2}{4} + \left(\frac{3 \cdot 500}{10^2}\right)^2} = 15.8113883008419 \]
The Slant Height of the Right Square Pyramid is 15.8113883008419 meters.
| Edge Length of Base (meters) | Volume (cubic meters) | Slant Height (meters) |
|---|---|---|
| 9 | 500 | 19.057427111777532 |
| 9.5 | 500 | 17.285932841759966 |
| 10 | 500 | 15.811388300841896 |
| 10.5 | 500 | 14.583228614685208 |
| 11 | 500 | 13.562006763644565 |