Geometry 11 2 Volumes of Prisms and Cylinders

hello class welcome to geometry lesson 11 1 which is all about volumes of prisms and cylinders by the end of this lesson you should be able to use the properties of prisms and cylinders to calculate their volumes so actually this is gonna be pretty short video because you guys have been doing this three years and don't think you need lot of my help with it so what I'm gonna do is I'm just gonna do quick overview introduce like the one new thing to you and then move on so example 1 develop Cavalier ease principle so you guys have actually done work with this before you just probably didn't know it was called Cavalier ease principle so basically what capillaries principle means is if have two items so in this case if you look at the picture have stack of paper and another stack of paper and we're gonna say that the heights of both these stacks are the same and they're made up of the same size they're actually calling on index cards okay so if were to tilt or like push some of the index cards so it formed slant there would these two stacks still represent the same volume and the answer is yes sometimes when you look at an image that's been tilted or slanted it gives this the kind of plays mind game on you and visually it looks like it would be different right just because it looks different however if the heights are the same and each like cross-section so in this case the index card would be cross section we learned about those yesterday if the cross sections are the same and the heights are the same that means that the two items actually have the same volume okay so like said that's called Cavalier ease principle and so the official wording is if two three-dimensional figures have the same height and same cross sectional area at every level then they have the same volume okay so it just kind of explains what talked about now this is great thing to take screenshot of it tells you how to find the volume of prisms and cylinders so the volume of the prism super easy it's volume equals the area of the base so whenever you see capital that doesn't just mean like base in the truck in 2d triangle no capital means the area of the base so in this case if we have this rectangle it'd be length times width so this capital represents that length times width if it was triangular base and say yes it was triangular prism or something something that looks like tent you would find the area of the triangle and then you'd multiply by the height so the area of the triangle would be represented by the capital and then lowercase for height the volume of cylinder same thing that you've been doing for years again the area of the base times the height or you can say PI squared times the height all right example to find the volumes of prisms and cylinders so this is just an example to show you how even if we had two jars where one was slanted you see how they have the same height if we were to do the math you would see that you take PI radius squared so my radius would be 10 centimeters times height and the height is 25 on the slanted one and the height is 25 on the regular one so it means they both have the same volume okay that's really all I'm gonna explain could do bunch of word problems but think you guys would get really bored and really frustrated with me if did that so here's your concept summary the volumes of prisms and cylinders Cavalier ease principle if you have questions at all please be sure to reach out for some help and I'm more than happy to assist you have great day