Understanding How to Calculate the Volume of a Square Pyramid: Step-by-Step Guide for Math Enthusiasts

Volume of a square pyramid

To find the volume of a square pyramid, you need to know the length of the base and the height of the pyramid

To find the volume of a square pyramid, you need to know the length of the base and the height of the pyramid. Let’s assume the base length is represented by ‘b’ and the height is represented by ‘h’.

The volume of a square pyramid (V) can be calculated using the formula:

V = (1/3) * b^2 * h

Here’s a step-by-step explanation of the formula:

1. Calculate the area of the base: Since the base of the pyramid is a square, the area can be found by squaring the length of one side. The formula for the area of a square is:

Area of the base = b^2

2. Multiply the area of the base by the height of the pyramid.

Volume = Area of the base * height
V = b^2 * h

3. Divide the result by 3.

Volume = (1/3) * b^2 * h

Let’s go through an example to illustrate this:

Example: Find the volume of a square pyramid with a base length of 5 units and a height of 8 units.

Step 1: Calculate the area of the base:
Area of the base = 5^2 = 25 square units

Step 2: Multiply the area of the base by the height:
Volume = 25 * 8 = 200 cubic units

Step 3: Divide the result by 3:
Volume = (1/3) * 200 = 66.67 cubic units

Therefore, the volume of the square pyramid is 66.67 cubic units.

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