Volume of a Pyramid
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.
below will explain more.
In the previous lesson, we learned that the volume of rectangular solid is
. Now, the volume of a pyramid is just one third of the rectangular solid's volume.
Hence, for a pyramid with width
, the volume,
of the pyramid will be:
The math video below will provide more explanations about this formula and will show some examples on using it.
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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.
on finding the volume of a pyramid
on finding the height of a pyramid
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