how to find the volume of a pyramid

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To calculate the volume of a pyramid, use the formula ${\displaystyle V={\frac {1}{3}}lwh}$ , where l and w are the length and width of the base, and h is the height. You can also use the equivalent formula ${\displaystyle V={\frac {1}{3}}A_{b}h}$ , where ${\displaystyle A_{b}}$ 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.

Volume Help

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]

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] 2 [3]}

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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.

4. 4

   Multiply your result so far by $$ 1 3 {\displaystyle {\frac {1}{3}}} . Or, in other words, divide by 3. Remember to state your answer in cubic units whenever you're working with three-dimensional space.^[4]

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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]

   • 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, ${\displaystyle V={\frac {1}{3}}lwh={\frac {1}{3}}A_{b}h}$ , so you need to know ${\displaystyle l}$ and ${\displaystyle w}$ first.
   • ${\displaystyle l={\text{width of pyramid base}}={\text{base of triangle, or}}\,b=2\,{\text{cm}}}$
   • ${\displaystyle w={\text{length of pyramid base}}={\text{height of triangle, or}}\,h=4\,{\text{cm}}}$

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: ${\displaystyle A_{b}={\frac {1}{2}}bh}$ .^[6]

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.

4. 4

   Multiply your result so far by $$ 1 3 {\displaystyle {\frac {1}{3}}} . 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] 3}

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Add New Question

• 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).

• Question

  How can I find the volume of a cone?

  

  Cone volume equals pi times radius times height divided by three.

• Question

  What if I have the pyramid's volume and height, but need to find the length and width?

  

  You could do that if the base is square, in which case you would triple the volume, then divide by the height and find the square root of the quotient, which would give you both the length and width of the square. If the base is not a square, you would have to know the length in order to find the width, or the width in order to find the length.

• Question

  What is the volume is a pyramid with the base edge of 16 cm?

  

  Assuming the pyramid has a square base, find the area of the base by squaring the edge. Multiply the area by the height of the pyramid, then divide by 3. That's the volume.

• Question

  How many digits does pi have?

  

  Actually, no one knows for sure. According to Wikipedia, pi can be expressed in "many trillions of digits."

• Question

  How do I find the volume of a pyramid where the height is 10' and the area of base is 62'?

  

  Use the second formula given in the introduction of the above article.

• Question

  How do I find the surface area of the pyramid?

  

• Question

  How can I find the length and width of a rectangular based pyramid if I have the volume and height, but no length or width?

  

  With that information, all you can find is the area of the rectangular base, not the length or width.

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• This method can be further generalized to such objects as pentagonal pyramids, hexagonal pyramids, etc. The overall process is: A) calculate the area of the base shape; B) measure the height from the tip of the pyramid to the center of the base shape; C) multiply A with B; D) divide by 3.

• In a square pyramid, the true height, slant height, and length of the edge of the base face are all related by the Pythagorean theorem: (edge ÷ 2)² + (true height)² = (slant height)²

• In all regular pyramids, the slant height, edge height, and edge length are also related by the Pythagorean theorem: (edge ÷ 2)² + (slant height)² = (edge height)²

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• Pyramids have three kinds of height --- a slant height, down the center of the triangular sides; a true height or perpendicular height, that goes from the tip of the pyramid to the center of the base face; and an edge height, that goes down one edge of the triangular sides. For volume, you must use the true height.

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Article SummaryX

To calculate the volume of a pyramid with a rectangular base, find the length and width of the base, then multiple those numbers together to determine the area of the base. Next, multiply the area of the base by the height of the pyramid. Take that result and divide it by 3 to calculate the pyramid's volume! To learn how to calculate the volume of a pyramid with a triangular base, read on!

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how to find the volume of a pyramid

Source: https://www.wikihow.com/Calculate-the-Volume-of-a-Pyramid

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