Calculating the Volume of a Pyramid and Cone: Formulas, Examples, and Explanations

Volume of a Pyramid/Cone

To find the volume of a pyramid or cone, you need to know the height and the base area

To find the volume of a pyramid or cone, you need to know the height and the base area.

For a pyramid, the volume formula is given by:
Volume = (1/3) * base area * height

For a cone, the volume formula is given by:
Volume = (1/3) * π * radius^2 * height

Let’s go through an example for both cases to illustrate how to use these formulas.

Example 1: Pyramid
Suppose we have a pyramid with a triangular base that has a base length of 6 units and a base width of 4 units. The height of the pyramid is 5 units.

1. Find the base area:
The base area of a triangle is given by:
Base area = (1/2) * base length * base width
Base area = (1/2) * 6 * 4 = 12 square units

2. Find the volume:
Using the volume formula for a pyramid:
Volume = (1/3) * base area * height
Volume = (1/3) * 12 * 5 = 20 cubic units

Therefore, the volume of the pyramid is 20 cubic units.

Example 2: Cone
Suppose we have a cone with a radius of 3 units and a height of 8 units.

1. Find the base area:
The base area of a cone is given by:
Base area = π * radius^2
Base area = π * 3^2 = 9π square units

2. Find the volume:
Using the volume formula for a cone:
Volume = (1/3) * π * radius^2 * height
Volume = (1/3) * π * 3^2 * 8 = 24π cubic units

Therefore, the volume of the cone is 24π cubic units.

Remember, for both the pyramid and cone, the volume is given in cubic units since it is a measure of three-dimensional space.

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