What is the volume of the pyramid 8 7 7

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To calculate the volume of a pyramid, use the formula

, where l and w are the length and width of the base, and h is the height. You can also use the equivalent formula

, where

is the area of the base and h is the height. The method varies slightly depending on whether the pyramid has a triangular or a rectangular base. If you want to know how to calculate the volume of a pyramid, just follow these steps.

1. 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're working with a square base, the method is the same, except the length and width of the square base will be equal. Write down these measurements.[1] X Research source Go to source

   • Remember,
     , so you need to know
     and
     first.

2. 2

   Multiply the length and width to find the area of the base. To get the area of the base, simply multiply 3 cm by 4 cm.[2] X Research source Go to source 2[3] X Research source Go to source

   • Remember, , so you need to know . You can find this by plugging in and from the previous step.

3. 3

   Multiply the area of the base by the height. The area of the base is 12 cm2 and the height is 4 cm, so you can multiply 12 cm2 by 4 cm.

   • Remember, , so you need to know
     . You can find this using from the previous step.

4. 4

   Multiply your result so far by

   . Or, in other words, divide by 3. Remember to state your answer in cubic units whenever you're working with three-dimensional space.[4] X Research source Go to source
   • Remember, . You can plug in
     from the previous step.

1. 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. They can also be considered the base and height of the triangle. In this example, the width of the base is 2 cm and the length of the triangle is 4 cm.[5] X Research source Go to source

   • If the length and width are not perpendicular and you don't know the height of the triangle, there are a few other methods you can try to calculate the area of a triangle.
   • Remember, , so you need to know and first.

2. 2

   Calculate the area of the base. To calculate the area of the base, just plug the base and height of the triangle into the following formula:

   .[6] X Research source Go to source
   • Remember, , so you need to know . You can find this using
     and
     from the previous step.

3. 3

   Multiply the area of the base by the height of the pyramid. The area of the base is 4 cm2 and the height is 5 cm.

   • Remember, , so you need to know . You can find this using from the previous step.

4. 4

   Multiply your result so far by . Or, in other words, divide by 3. Your result will show that the volume of a pyramid with a height of 5 cm and a triangular base with a width of 2 cm and a length of 4 cm is 6.67 cm.[7] X Research source Go to source 3

   • Remember, . You can plug in
     from the previous step.

• Question

  How do I calculate the volume of a three square tier pyramid?

  Determine the area of the base. If it is a rectangle, that's length x width, if it is a triangle it's 1/2 x the base (one side) x the height (a line perpendicular to the base to the opposite vertex). Determine the height of the pyramid. It is a line perpendicular (straight up) from the base of the pyramid to the opposite vertex. Muliply (1) x (2) and divide by 3. The formula is 1/3 x the area of the base x the height of the pyramid

• Question

  How do I find the height if given the volume and the base length for a square pyramid?

  Triple the volume and divide that by the area of the base (which is the square of the length of an edge).

• Question

  How do I double the volume of a square pyramid?

  Either double the height of the pyramid or double the area of the base. Accomplish the latter by multiplying the length of each side of the base by the square root of 2 (1.414).

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Co-authors: 50

Updated: June 28, 2022

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Categories: Featured Articles | Volume

Article SummaryX

To calculate the volume of a pyramid, you need to know its height and the area of the base. Once you have that information, you can find the volume using the formula V (volume) = 1/3 x Ab (the area of the base) x h (height). If the pyramid has a square or rectangular base, simply multiply the width of the base by its length to find the area. Then, multiply the area of the base by the height of the pyramid, and multiply the result by 1/3—which is the same as dividing by 3. For instance, if your pyramid has a square base that is 3 inches long by 3 inches wide, and a height of 4 inches, the volume would be (3 x 3 x 4)/3, or 12. Since you’re describing the volume of a 3-dimensional object, remember to write your answer in cubic units. In this case, the pyramid has a volume of 12 cubic inches. For pyramids with a triangular base, the technique is a little different. If you know the triangle’s height and the width of its base, plug those numbers into the formula ½ x b (base) x h (height) to find the area of the triangle. From there, you can use the same formula that you used for the square-based pyramid. For example, say your pyramid has a base that’s a triangle with a base width of 2 cm and a height of 4 cm, and the pyramid has a height of 6 cm. First, find the area of the triangle using the formula ½ x 2 x 4, which will give you a base area of 4 square centimeters. Next, multiply the area by the height of the pyramid, then multiply the product by 1/3. In this case, 6 x 4 x 1/3 = 8, which means the pyramid has a volume of 8 cubic centimeters. To learn how to calculate the volume of a pyramid with a triangular base, read on!

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