Volume of a Pyramid Math with Mr J

Welcome to Math with Mr. In this video, I'm going to cover how to find the volume of pyramid. And remember, volume is the amount of space that 3D figure or object takes up. Now, when it comes to pyramids, we can use the formula 1/3 times the area of the base times the height. So, whatever the base is, rectangle, square, triangle, etc., use the correct formula to find that area and then plug the area of the base into the formula for the volume. Now, do want to mention that you can also use the formula the area of the base times the height and then divide by three. Because multiplying by 1/3 is the same as dividing by three. Now, we'll talk about why we multiply by 1/3 or divide by three after number one. Knowing why we do this will give us better understanding of the formula. So, let's jump into number one where we have pyramid with square base and then height of 4 in. So, the first thing that we need to do is write out our formula. So, volume equals 1/3 times the area of the base times the height. Once we have that, we can plug in. So, volume equals 1/3 times the area of the base. Well, we have square, so we can do 6 * 6 to calculate the area of that base. 6 * 6 gives us 36. times the height of four. Now, do want to mention we were able to calculate the area of that base using mental math. Don't be afraid to come to the side though in order to write things out or for more difficult problem. So, for example, let's go to the bottom left where we have some room. We could have gone area equals side length squared. Well, that's the formula for the area of square and then plug in. side length of 6 squared, which means 6 * 6 gives us an area of 36 sq in. So, again, don't So, again, don't be afraid to come to the side if you need to calculate something and then plug that area into the formula. So, now we're ready to solve. 1/3 * 36 * 4. Now, at this point, you can plug this all into calculator and solve it all in one step, but want to break it down step by step until we get to that final volume. Well, 1/3 * 36, that's going to give us 12. times four to wrap things up here. So, 12 * 4 gives us 48 and this is cubic inches for our unit of measure there. So, volume equals 48 cubic inches for our final answer. Now, do want to show you what the other formula looks like as well for number one. So, the area of the base times the height and then divide by three. So, we have volume equals the area of the base times the height and divide by three. So, let's plug in. Volume equals the area of the base was 36 times the height of four and divide by three. So, I'm running out of room there. I'm going to go to the side in order to solve this. So, 36 * 4 gives us 144 divided by three and that's going to give us final answer of cubic inches. So, we got the same answer either way as far as those two formulas. So, multiplying by 1/3 is the same as dividing by three. Both of those are going to give us the correct volume. Now, do want to talk about why we multiply by 1/3 or divide by three to help us better understand this formula. So, if we take our pyramid, put it in prism with the same base and height, let me try to draw that so we can visualize what mean. So, prism with the same base and same height. Now, this won't be the best drawing, but think it will get the point across here. So, think of it like putting it in box with the same exact height and base. So, we put the pyramid in prism again with the same base and height. That pyramid is going to be exactly 1/3 the volume of that prism. Now, we find the volume of prism by using the formula the area of the base times the height. So, the exact same thing as the pyramid formula, but without the 1/3 or divide by three. And again, we multiply by 1/3 or divide by three because pyramid is exactly 1/3 the volume of prism with the same base and height. So, let's move on to number two where we have pyramid with rectangular base and height of 11 And the first thing that we need to do, write out the formula. So, volume equals 1/3 times the area of the base times the height. Now, we plug in. So, 1/3 times the area of the base. Well, we have rectangle, so we can do length times width. So, 8 * 7, that gives us 56 times the height of 11 So, now we're ready to solve 1/3 * 56 * 11. Now, I'm going to do 56 * 11 first for number two. Unlike number one where we had something compatible with that 1/3, we had 1/3 * 36 and got nice clean whole number of 12. In the case of number two, we don't have anything compatible with that 1/3. So, again, 56 * 11 is what I'm going to do first here and that's going to give us 1/3 times 16. Now, 1/3 * 616 is going to give us an answer of 205 and I'm going to round this decimal to the nearest hundredth. 33 hundredths and this is cubic meters. So, our final answer, 205 and 33 hundredths cubic meters. So, there you have it. There's how you find the volume of pyramid. 1/3 times the area of the base times the height or the area of the base times the height and then divide by three. hope that helped. Thanks so much for watching. Until next time, peace.