Volume of a Pyramid
Volume of any pyramid.
Formula
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Example
Square base 6×6 (B=36), height 10: V = (1/3)·36·10 = 120.
How it works
A pyramid takes up one-third of the space of a prism that has the same base area and the same height. That is why its volume is found by multiplying the base area by the vertical height and then dividing by 3. The height must be the perpendicular distance from the apex to the base, not a slanted edge.
When to use it
Use this formula when finding the amount of space inside a pyramid-shaped solid, such as a square pyramid, triangular pyramid, or a roof-like pyramid form. It appears in geometry problems, design measurements, and any situation where you know the base area and vertical height.
Worked example, step by step
A pyramid has a rectangular base measuring 8 m by 5 m, and a vertical height of 9 m. Step 1: Find the base area: B = 8 × 5 = 40 m² Step 2: Use the volume formula: V = (1/3)Bh Step 3: Substitute the values: V = (1/3) × 40 × 9 Step 4: Calculate: V = 120 m³ Final answer: The volume of the pyramid is 120 cubic metres.
Common mistakes to avoid
- Using the slanted side length instead of the perpendicular height
- Forgetting to find the base area first when the base is not already given as an area
- Leaving out the division by 3 and treating it like a prism
Did You Know?
Like the cone, a pyramid is one-third of its enclosing prism — the Egyptians knew this empirically.
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