Finding Volume with Unit Cubes How to Find Volume

Welcome to Math with Mr. In this video, we're going to be finding volume using unit cubes. And if you take look at your screen, we have two rectangular prisms that are filled with unit cubes. So, we have great visual of what volume is. That's why like these unit cubes, especially when someone's just starting out taking look at volume. also have our formulas up here that we can use for volume. And using these unit cubes will give us better understanding of why and how those work. So, let's jump right into number one here where we have rectangular prism filled with the unit cubes. So, the first thing we need to do There's couple different strategies. Let's use the base * height formula first. So, I'm going to write my formula. Volume equals base, the area of the base, times the height. So, what this means, essentially, find how many cubes make up one layer of that rectangular prism. It doesn't matter if it's the top, bottom, either will work. So, let's do the top layer. Count how many cubes are on that top layer. Hopefully, you got to the answer of 15. That's the area of the base, our area of one of the layers, is 15. Now, we can find the volume, or how many unit cubes take up that shape, by multiplying one layer by how many layers there are. And there's one, two, three layers. So, we could do 15 * 3, and that will give us how many unit cubes make up that rectangular prism. And 15 * 3 gives us 45. And will put cu, which means cubic units. And that's the volume of that rectangular prism. And volume is how much space three-dimensional object takes up. Let's use our other formula and see if we get the same answer. Volume equals length * width * height. So, length consider how far back the three-dimensional object goes. So, if we take look here, how many cubes back? Well, three. * the width. How wide? Five unit cubes. And lastly, how tall, the height? Three unit cubes. And this will get to 3 * 5 is 15, * that 3 gives us 45 cubic units. So, both formulas give us the same answer. And that will happen for every rectangular prism. Again, volume is how much space three-dimensional object takes up, and we use unit cubes in order to measure that space, whether it's cubic inches, cubic feet, cubic yards, meters. Here, we're just using cubic units. The unit of measure's not given. So, let's take look at number two. So, we have rectangular prism there. We're going to find out the volume by finding how many cubic units cubic units fill that rectangular prism. So, again, two formulas we can use. We'll go through both. Volume equals the area of the base times the height. So, for this one, you find the area of one of the layers, and then multiply it by how many layers there are. So, let's take look at the top layer. How many unit cubes make up that top layer? Hopefully, you're thinking eight. So, one layer has eight cubes, and then multiply it by the height, or how many layers there are. One, two, three, four layers. So, 8 * 4 gives us volume of 32 cubic units. Let's do length * width * height as well. So, write out our formula, then we plug in. So, how far back, what is the length? One, two, three, four. * the width here, which is one, two. And the height we already already determined is one, two, three, four. So, we get to volume of 4 * 2 is 8, * 4 is 32 cubic units. So, using unit cubes gives us visualization of volume and what it means to fill rectangular prism with unit cubes. So, hopefully that helped. Thanks so much for watching. Until next time. Peace.