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Square Pyramid Base Length Formula:
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The formula \( L = \sqrt{\frac{3V}{H}} \) calculates the base length of a square pyramid from its volume and height. This is derived from the volume formula for a square pyramid: \( V = \frac{1}{3}L^2H \).
The calculator uses the formula:
Where:
Explanation: The formula is derived by solving the standard pyramid volume formula \( V = \frac{1}{3}L^2H \) for the base length L.
Details: Calculating the base length is essential in architecture, engineering, and geometry problems where you know the volume and height of a square pyramid but need to determine its base dimensions.
Tips: Enter the volume in cubic units and height in units. Both values must be positive numbers. The calculator will compute the base length in the same units as the height.
Q1: What units should I use for the calculation?
A: Use consistent units for all measurements. The volume should be in cubic units and height in linear units. The result will be in the same linear units as the height.
Q2: Can this formula be used for rectangular pyramids?
A: No, this formula is specifically for square pyramids where the base is a perfect square. For rectangular pyramids, you would need both length and width dimensions.
Q3: What if I have the slant height instead of the vertical height?
A: This formula requires the vertical height (perpendicular from apex to base). If you have the slant height, you'll need to use the Pythagorean theorem to find the vertical height first.
Q4: How accurate is this calculation?
A: The calculation is mathematically exact for perfect square pyramids. The accuracy of your result depends on the precision of your input measurements.
Q5: Can this calculator be used for truncated pyramids (frustums)?
A: No, this calculator is designed for complete square pyramids. Different formulas are needed for truncated pyramids.