### 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:

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

### Math Video

#### Lesson Video

Sponsored Links

Volume of a Pyramid from MathExpression.com on Vimeo.

You can contribute to the development of this site and keep it free by getting all six video lessons and volume of solids and calculator app for just US$1.99 from Apple App Store.

I'd like to contribute or to know more about the app#### Math Video Transcript

00:00:03.170

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

00:00:15.090

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

00:00:21.080

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

00:00:29.180

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

00:00:36.190

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

00:00:43.190

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

00:00:47.160

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

00:00:56.130

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

00:01:05.060

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.

00:01:18.090

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

00:01:25.130

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

00:01:32.090

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

00:01:38.110

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

00:01:43.100

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

00:01:49.190

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

00:01:58.210

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

00:02:03.170

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

00:02:09.090

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

00:02:15.080

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

00:02:25.240

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

00:02:33.070

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.

00:02:43.150

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.

00:02:55.120

1wlh is the same as, wlh.

00:03:01.020

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

00:03:06.240

This gives, 3V = wlh.

00:03:13.030

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

00:03:23.210

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

00:03:29.160

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

00:03:36.020

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

00:03:42.230

Now, we have, 6h equals to 30.

00:03:47.190

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

00:03:52.230

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

00:03:57.130

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

00:04:02.160

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

00:04:11.150

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

00:04:16.180

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

00:04:22.040

Hence, the height of this pyramid is 5ft.

00:04:27.020

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

#### Site-Search and Q&A Library

Please feel free to visit the Q&A Library. You can read the Q&As listed in any of the available categories such as Algebra, Graphs, Exponents and more. Also, you can submit math question, share or give comments there.