Volume of Rectangular Prisms Math with Mr J

Welcome to Math with Mr. In this video, I'm going to cover how to find the volume of rectangular prism. Remember, volume is the amount of space an object takes up. Now, for any prism, we can use the formula volume equals the area of the base times the height. The capital stands for the area of the base, and then the stands for the height. But, since we're going to specifically be working with rectangular prisms, we know that our base will be rectangle. The formula for the area of rectangle, which again is our base, is length times width. So, we can use the formula length times width times height for rectangular prisms. So, instead of the capital we can be more specific and put in length times width. Let's jump into our examples here, starting with number one, where we have rectangular prism with base with dimensions of 5 in and 4 in, and then height of 12 in. We'll start by writing out our formula. So, volume equals length times width times height. Our next step, we need to plug in our length, width, and height. Now, never get too held up on which dimension is the length of our base and which is the width of our base. As long as we are using the 5 in and the 4 in, we're going to get the correct area of that base and therefore the correct volume of the rectangular prism. I'm going to use the longer dimension, five, for our length and the shorter dimension, four, for our width in order to keep things consistent. So, that's common way of doing things when it comes to length and width, using the longer dimension for length and then the shorter for the width. But again, don't get too held up on this because 5 * 4 = 20 and 4 * 5 = 20. So, either way, you're going to get the correct area of the base, which is going to be 20 sq in. So, let's plug in the length and width here. So, the length of five times the width of four times our height of 12 here. So, 5 * 4 * 12 is going to give us the volume of this rectangular prism. So, let's do one step at time here. 5 * 4 gives us 20. That's the area of our base, and then multiply it by the height of 12. So, 20 * 12, that's going to give us 240. Now, Now, we need to remember our unit of measure here. Our answer represents how many cubic units fill our rectangular prism. So, for number one, we have cubic inches. So, we can put inches and then cubed. So, 240 cubic inches as far as the volume of number one. Let's move on to number two, where we have another rectangular prism, but for this one, we have more sides that are labeled. So, we really need to know what we're looking for here as far as length times width times height. Don't just multiply all of the numbers that you are given. We need to be very careful here. So, let's write out our formula. Volume equals length times width times height. So, now we need to plug in the length and width of our base. So, for the length, I'm going to use the longer dimension here of 20 cm, and then for the width, I'm going to use the shorter dimension here of 18 cm. So, let's plug those in. Volume equals length 20 cm times the width of 18 cm times the height of 9 cm. So, we picked out our length, width, and height. Now, remember, don't get too held up on the length and width. If you were to use 18 for your length and 20 for your width, you're still going to get the correct answer. So, now let's do one step at time here. 20 * 18, that's going to give us 360. And then we can multiply that by our height of nine. So, the area of the base is 360, and then multiply that by nine to get our final volume, and that's going to be 3,000 240. And we are working with cubic centimeters. Final volume, 3,240 So, there you have it. There's how you find the volume of rectangular prism. Volume equals length times width times height. hope that helped. Thanks so much for watching. Until next time, peace.