Picture of a Pyramid

Formula Volume of a Pyramid

Pyramid's Volume

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.

Picture of Formula of a Pyramid

Practice Problems: Volume of Pyramid

Problem 1

What is the volume of the pyramid in the picture below?

Volume of Pyramid problem

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?

Volume of Pyramid problem

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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