Formula for the Volume of a Pyramid
The volume of a pyramid equals $$ \frac{1}{3} $$ the area of its base times its height. This formula applies to both regular and irregular pyramids.
Practice Problems: Volume of Pyramid
Problem 1
What is the volume of the pyramid in the picture below?
Use the formula for the volume of a pyramid.
Volume = $$\frac{1}{3} \text{(area of base)} \cdot \text{height} $$
Area of base = $$15 \cdot 14= 210 $$
Volume = $$\frac{1}{3}(210)(12) = 840$$
Problem 2
What is the volume of the pyramid in the picture below?
Use the pyramid volume formula.
Volume = $$ \frac{1}{3} \text{(area of base)} \cdot \text{height} $$
Volume = $$ \frac{1}{3} \text{(area of base)} \cdot \text{(height) } $$
Area of base = $$4 \cdot 12 $$
Volume = $$ \frac{1}{3}$$ (48)(8) = 128
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