Volume of a Pyramid

Lesson Objective

In this lesson, we will learn about the volume of a pyramid.

About This Lesson

In this lesson, we will:

Learn about the formula for the volume of a pyramid.
See an example on using the formula to calculate a pyramid's volume.
See another example on using the volume formula to find the height of a pyramid.

The study tips and math video below will explain more.

Study Tips

Tip #1

In the previous lesson, we learned that the volume of rectangular solid is wlh. Now, the volume of a pyramid is just one third of the rectangular solid's volume.

Hence, for a pyramid with width w, length l and height h, the volume, V of the pyramid will be:

a pyramid with width w, length l and height h

The math video below will provide more explanations about this formula and will show some examples on using it.

Math Video

Lesson Video

Math Video Transcript

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In this lesson, we will learn about the volume of a pyramid. Consider this pyramid.

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Now, this pyramid has the width w, length l, and height h.

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With this, the formula for the volume of this pyramid, V = 1/3(wlh).

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Here, note that, 'wlh' is actually the volume of a rectangular solid.

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Hence, the volume of a pyramid is actually one third of the volume of a rectangular solid.

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Let's see some examples on how to use this formula.

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This pyramid has the width 4cm, length 5cm, and height 3cm. Find its volume.

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To find the volume, we use the formula for the volume of a pyramid, V equals to 1/3(wlh).

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Now, since the width is given as 4cm, we can substitute w with 4. Similarly, since the length is given as 5cm. we can substitute l with 5.

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Now, we can simplify by multiplying 4 with 5. This gives 20.

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Next, since the height is given as 3cm, we can substitute h with 3

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Let's continue to simplify by multiplying 20 with 3. This gives 60.

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Alright, now we have 1/3(60).

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Note that, this term is the same as, 1 bracket 60 over 3.  

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1 multiply by 60 gives back 60. Next, 60 divides by 3, gives 20.

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Now, this number has no meaning unless we include the unit for it.

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Since the units are given in centimeter, the unit for volume will be in cubic centimeter.

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Hence, the volume of this pyramid is 20 cubic centimeter.

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Next example, the volume of this pyramid is 10 cubic feet. Its width is 2ft, and length is 3ft. Find its height, h.

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We can begin by using the formula for the volume, V = 1/3(wlh).

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Here, since the volume, width, and length are given, we can find the height of the pyramid, h, by solving the equation for h. Here’s how.

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First, note that, it is easier to work with this equation if we change 1/3(wlh), to the form of fraction, 1wlh, over 3.

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1wlh is the same as, wlh.

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Next, we can remove this fraction by multiplying both sides of the equation with 3.

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This gives, 3V = wlh.

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Now, since the volume is given as 10 ft, we can substitute V with 10. 3 multiply by 10, gives 30.

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Since the width is given as 2 ft, we can substitute w with 2.

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Similarly, since the length is given as 3 ft, we can substitute l with 3.

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Here, we can simplify by multiplying 2 with 3. This gives 6.

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Now, we have, 6h equals to 30.

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Let's rewrite this equation, so that it looks neater.

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Next, to find h, we need to remove 6.

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To do so, we can divide both sides of the equation with 6.

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This gives, h equals to 30 over 6. 30 divide by 6, gives 5.

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Again, this number has no meaning unless we include the unit for it.

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Since the volume is in cubic feet, the height of the pyramid will be in feet.

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Hence, the height of this pyramid is 5ft.

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This is all for this lesson. Try out the practice question to further your understanding.

Practice Questions & More

Multiple Choice Questions (MCQ)

Now, let's try some MCQ questions to understand this lesson better.

You can start by going through the series of questions on the volume of a pyramid or pick your choice of question below.

Question 1 on finding the volume of a pyramid
Question 2 on finding the height of a pyramid

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