To calculate the volume of a pyramid, all you have to do is find the product of the base and the height of the pyramid and multiply the result by 1/3. The method is slightly different depending on the base of the pyramid, whether it is a triangle or a quadrilateral. If you want to know how to calculate the volume of a pyramid, follow these steps.
Step
Method 1 of 2: Pyramid with a Square Base
Step 1. Find the length and width of the base
In this example, the length of the base is 4 cm and the width is 3 cm. If you calculate the base of a square, the method is the same, except that the length and width of the square base are the same length. Write down this calculation.
Step 2. Multiply the length and the width to find the area of the base of the pyramid
To calculate the area of the base, multiply 3 cm by 4 cm. 3cm x 4cm = 12cm2
Step 3. Multiply the area of the base by the height
The area of the base is 12 cm 2 and the height is 4 cm, so you can multiply 12 cm2 by 4 cm. 12 cm2 x 4cm = 48cm3
Step 4. Divide the result by the number 3
This is tantamount to multiplying the result by 1/3. 48cm3/3 = 16 cm3. The volume of a pyramid with a height of 4 cm and a base with a width of 3 cm and a length of 4 cm is 16 cm3. Remember to write your answer in cubic units when calculating three-dimensional space.
Method 2 of 2: Pyramid with Triangle Base
Step 1. Find the length and width of the base
The length and width of the base must be perpendicular to each other for this method to work. Or it can also be referred to as the base and height of the triangle. In this example, the width of the triangle is 2 cm and the length is 4 cm. Write down this calculation.
If the length and width are not perpendicular and you don't know the height of the triangle, there are other ways you can try to calculate the area of the triangle
Step 2. Calculate the area of the base
To calculate the area of the base, plug the length of the base and the height of the triangle into the following formula: A = 1/2(a)(t).
Here's how to calculate it:
- L = 1/2(a)(t)
- L = 1/2(2)(4)
- L = 1/2(8)
- L = 4 cm2
Step 3. Multiply the area of the base by the height of the pyramid
The area of the base is 4 cm2 and its height is 5 cm. 4 cm2 x 5 cm = 20 cm3.
Step 4. Divide the result by 3
20 cm3/3 = 6.67 cm3. Thus, the volume of a pyramid with a height of 5 cm and a base of a triangle with a width of 2 cm and a length of 4 cm is 6.67 cm3
Tips
- In a quadrilateral pyramid, the height, hypotenuse, and the length of the side of the base correspond to the Pythagorean theorem: (side 2)2 + (height)2 = (slope side)2
- In all ordinary pyramids, the hypotenuse, edge height, and edge length are also related to the Pythagorean theorem: (edge length 2)2 + (sloping side)2 = (edge height)2
- This method can also be used with other shapes such as pentagon pyramids, hexagon pyramids, and so on. The whole process is: A) calculating the area of the base; B) measure the height from the end of the pyramid to the center of the base; C) multiply A by B; D) divided by 3.
