Volume of Rectangular Prisms 7 th Grade Math Lesson

hey guys today we are going to answer the question how do find the volume of rectangular prisms so rectangular prism is shape that has six rectangular faces where the opposite faces are parallel and congruent rectangular prisms are special because any two of the opposite faces can be used as the bases you just have to make sure whatever you use as the base is that you're using the height as the distance that connects the bases and remember to find the area of rectangle we're going to multiply the base and the height of the rectangle which you'll need to use for the formula the formula for the volume of rectangular prism is equals capital times where that capital is the area of the base so to find the volume we will take the area of the base the area of that rectangular base which will do BH to find and we will multiply it by the height of the prism am going to be shading the bases green and then I'll be circling the height in pink so let's go ahead and do that here the base can be any of the opposite faces could use these as the base if I'm going to do that then this needs to be the height could use the bottom and the top as the base if I'm going to do that then this distance needs to be the height and you could even use the front and the back as the bases you just need to make sure that you use this distance connecting the front into the back as the height I'm going to use the sides for this picture right here I'm going to use those as the bases which then would make the distance between them right here the height so again to find the volume of rectangular prism we're going to multiply the area of the rectangular base that will shade in green or all shade in green and then multiply it by the height of the prism so very first thing you want to do is identify your bases and your height on this one I'm going to use the bottom and the top as my bases and then that makes my height 13. so to find the volume of prism I'm going to do equals capital times and remember is the area of that green base that just shaded for this one I'm going to draw out picture of the rectangular base it is six by seven rectangle so to find the area of the base I'll do 6 times 7 which is 42. so to find the volume I'm going to do 42 my base times that height of 13 that connected my bases and now I'm going to multiply 42 times 13. and get that the volume of this shape the area of the base times the height is 546 and this would be centimeters cubed because the volume is the amount of 3D space that would fill that shape okay let's look at this next one it says find the volume of the rectangular prism very first thing we want to do is decide our bases so this time I'm going to use the sides as my bases which means that 22 is the height so I'm going to find the volume by doing area of the base times the height so first thing want to do is find capital area of the base by multiplying the base and the height of that rectangle so it's going to be 4 times 1.5 so the area of the base is 6. so to find the volume just found the area of the base it was 6 and now I'm going to multiply that by the height of 22. so just need to do 6 times 22 to find the volume of this shape and the volume of this shape will be 132 inches cubed okay let's look at number three first thing want to do is identify the base and the height this time I'm going to use this side and this side as my base is which makes 6 or sorry eight the height because that's connecting my bases so now need to do the area of this because the volume of rectangular prism can be found by doing the area of the base times the height so need to find the area of the green base first and this length is the same as this one right here so it's three so need to do 14 times 3 to find the area of the base and 14 times 3 is 42 so the area of the base is 42. so to find the volume will do 42 times the height the distance between the two bases which was eight so now I'm going to find the volume by doing 42 times 8. and get that the volume is 336 yards cubed okay another rectangular prism I'm going to find the volume of by doing the area of the base times the height so let's recognize our bases first I'm going to use the bottom and the top as my bases this time which means need to use 15 as the height so the first thing need to do is find capital the area of that base that shaded so I'm going to do 7 times 5. and get 35 for the base so to find the volume will do the air of the base which is 35 times the height which is 15. so just need to do 35 times 15 to find the volume and get that the volume of this prism is 525 feet cubed okay number five says the volume of rectangular prism is 468 meters cubed the area of the base is 36 meters squared what is the height so let's write out our formula it is equals and then let's write out what they gave us so they told us the volume is 468 meters cubed they gave us capital the area of the base is 36 meters squared so capital is 36. and they are asking us what is the height so can set up an equation with this information and then use that equation to solve for the missing height so the volume like found was 468 equals the area of the base was 36 and then the height is what I'm looking for so I'm going to leave it as so the last thing need to do to identify is just undo this times 36 so I'm going to divide by 36. so 468 divided by 36 will tell me the height of this prism so the height of this prism is 13 meters okay let's look at number six Joey purchases an aquarium in the shape of rectangular prism for his Turtle the aquarium measures 24 inches long eight inches wide and 10 inches tall Joey fills the aquarium halfway with water how many cubic inches of water are in Joey's aquarium so we need to find the volume and then the keyword is halfway we only want half of the volume so after we find the volume we're going to divide it by two so let's start by finding the volume of his aquarium that's rectangular prism so need to do the area of the base times the height so I'm going to go ahead and use 10 as the height since they told us that it's 10 inches tall and then that means that 24 and 8 make up my base I'm going to draw out the base here it would be an 8 by 24 base so to find the base the area of the base I'm going to do 24 times 8. and get 192 for the area of the base so to find the volume of the whole aquarium would take the area of the base which was 192 and multiply it by the height of 10. so that means the volume of the whole aquarium is hundred or 1920. now remember only wanted half of the volume because we're only filling it halfway so now I'm going to divide this by 2 to determine the volume that it would take to fill up half of it so the volume that it would take to fill up half of the aquarium would be 960 inches cubed