Pyramid Volume Calculator
Calculate the volume of a rectangular pyramid: V = (1/3) × l × w × h
Enter Base Dimensions and Height
Step-by-Step Solution:
1. Formula: V = (1/3) × base area × height
2. Base area: l × w = 6 × 4 = 24 square units
3. Multiply by height: 24 × 9 = 216
4. Divide by 3: 216 / 3 = 72.00 cubic units
Pyramid Volume Formula
Volume = (1/3) × base area × height
For a rectangular pyramid: V = (1/3) × l × w × h
where: - l = length of the rectangular base - w = width of the rectangular base - h = perpendicular height from the base to the apex
How to Calculate Pyramid Volume
- Measure the base: Find the length and width of the rectangular base
- Calculate base area: Multiply length × width
- Measure the height: Find the perpendicular distance from the base to the apex
- Multiply: base area × height
- Divide by 3: The volume is one-third of base area × height
Understanding the Pyramid
A pyramid has a polygonal base and triangular faces that meet at a single point (apex). The volume is always one-third of the volume of a prism with the same base and height. This 1/3 factor applies to all pyramids regardless of the base shape.
The Egyptian pyramids at Giza are the most famous examples of rectangular pyramids, though they are close to square-based pyramids where l ≈ w.
Real-World Applications
Pyramid volume calculations are used in: - Architecture: Pyramid-shaped roofs and monuments - Construction: Estimating materials for pyramid structures - Mining: Stockpile volume estimation - History: Studying ancient pyramid construction - Packaging: Pyramid-shaped containers
Common Questions
What is the formula for pyramid volume?
The pyramid volume formula is V = (1/3) × base area × height. For a rectangular base, this becomes V = (1/3) × length × width × height.
Why is pyramid volume one-third of a prism?
A pyramid has exactly one-third the volume of a prism with the same base and height. This is because the pyramid tapers to a point, reducing its cross-sectional area linearly from base to apex.