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

If the above player doesn't work, try this direct link.

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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