Volume of a Triangular Pyramid | Math with Mr. J - By Math with Mr. J
Transcript
| 00:0-1 | Welcome to Math with Mr J . In this video | |
| 00:05 | , I'm going to cover how to find the volume | |
| 00:07 | of a triangular pyramid . And remember volume is the | |
| 00:11 | amount of space that a three D . Figure or | |
| 00:13 | object takes up . Now when it comes to pyramids | |
| 00:17 | we can use the formula one third times the area | |
| 00:20 | of the base , times the height . So whatever | |
| 00:23 | the base is a rectangle , a square . In | |
| 00:26 | the case of this video , a triangle , find | |
| 00:28 | the area of that base using the correct formula and | |
| 00:32 | then plug that area into the formula for the volume | |
| 00:36 | . I do want to mention that you can use | |
| 00:38 | the formula . The area of the base times the | |
| 00:41 | height divided by three because multiplying by one third and | |
| 00:46 | dividing by three will give you the same thing . | |
| 00:49 | So let's jump into our example where we have a | |
| 00:52 | triangular pyramid with a height of 10 inches . And | |
| 00:55 | the first thing that we want to do is write | |
| 00:58 | out our formula . So volume equals One 3rd times | |
| 01:06 | the area of the base , times the height . | |
| 01:09 | Now we plug in so volume equals 1/3 . Now | |
| 01:15 | we need to calculate the area of the base . | |
| 01:19 | So this triangular base right here and we're going to | |
| 01:22 | go off to the side in order to calculate this | |
| 01:25 | . So we can use the formula area equals one | |
| 01:29 | half times the base times the height . Or you | |
| 01:35 | can do base times height , divided by two , | |
| 01:37 | multiplying by a half or dividing by two . They | |
| 01:40 | will get you the same answer . So let's plug | |
| 01:43 | in Our base of the triangle and the height . | |
| 01:46 | So one half Times the base , which is seven | |
| 01:53 | times the height of eight inches . So we know | |
| 02:01 | that seven times eight is 56 . So let's break | |
| 02:05 | this down here And we'll do one half times 56 | |
| 02:09 | or one half of 56 . And that gives us | |
| 02:12 | an area of 28 . So the area of the | |
| 02:17 | base is 28 square inches . So let's plug that | |
| 02:21 | in Times the height of 10 And now we're ready | |
| 02:28 | to solve here . So one third times 28 times | |
| 02:32 | 10 , that's going to give us the volume of | |
| 02:35 | this triangular pyramid . So let's break this down and | |
| 02:40 | we'll do 28 times 11th , 28 times 10 is | |
| 02:44 | going to give us 280 And we'll wrap this up | |
| 02:48 | with 1/3 times 280 or 1/3 of 280 . And | |
| 02:53 | that gives us a final volume of 93 . And | |
| 02:58 | I'm going to round this decimal to the nearest 100th | |
| 03:02 | . So 33/100 And this is volume , so cubic | |
| 03:06 | inches . So our final volume 93 and 33/100 cubic | |
| 03:14 | inches . And again I rounded that decimal to the | |
| 03:16 | nearest 100th . Now I'm also going to solve this | |
| 03:20 | using the other formula , the area of the base | |
| 03:23 | times the height divided by three essentially both of those | |
| 03:26 | are the same thing . Remember multiplying by one third | |
| 03:29 | and dividing by three will get you the same thing | |
| 03:32 | but I'll set it up to show you how that | |
| 03:34 | works as well . So we will write out our | |
| 03:37 | formula . So area of the base times the height | |
| 03:41 | divided by three . Now we plug in So the | |
| 03:45 | area of the base while we said that was 28 | |
| 03:48 | . We already solved for that times the height of | |
| 03:52 | 10 And divide that by three . So we end | |
| 03:56 | up with 28 times 10 is 280 , Divide that | |
| 04:03 | by three . To get our final answer of The | |
| 04:06 | same thing 93 . And again I'm rounding to the | |
| 04:10 | 100th place 33 I'll put my unit of measure underneath | |
| 04:15 | because I'm running out of room here . So 93 | |
| 04:19 | 33/100 cubic inches so there you have it . There | |
| 04:24 | is how you find the volume of a triangular pyramid | |
| 04:26 | , one third times the area of the base , | |
| 04:30 | times the height or the area of the base times | |
| 04:33 | the height divided by three . I hope that helps | |
| 04:37 | . Thanks so much for watching until next time . | |
| 04:40 | Peace . Yeah . Yeah . Yeah . |
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