Volumes of Prisms and Cylinders Formula Examples

hi this is Mario with Mario's math tutoring coming to you with another math video to help you boost your score in your math class improve your understanding and hopefully make math more fun and less stressful so in this video what we're going to talk about is how to find the volume of prisms and cylinders okay so what is prism okay and what is cylinder well prism is basically three dimensional object okay where you've got two bases okay that are the same size and shape okay they're so they're congruent and they're parallel meaning if they were to keep going they're not going to cross so they're parallel congruent bases separated by the height okay so that's what prism is cylinder is basically the exact same thing okay it looks like can of some sort you can almost think of it as circular prism the top and bottom are circles okay and it's separated by the height okay and the two circles are parallel and congruent so the formulas really easy it's the area of the base times the height so the capital means the area of the base so not the length of the base but the actual two-dimensional area times the height so what you could think of is you could think of this as triangle and you're stacking up these triangles on top of one another until you get three-dimensional object so it's like sticky notes you know notepad you stack them up that gives you the third dimension that gives you the volume three-d right okay so if we find them let's look at this example if we find the volume of this triangular prism okay now notice the the dots here the dashes that just means that we're looking through the object to the other side so that we can kind of get that sense of 3d on flat surface okay but let's go and find the volume on this one it's the area of the base times the height now what like to do is like to write down the formula and you might want to do the same thing too but then what we can do is we can subdivide the formula so the area of the base that's triangle what's the formula for area of triangle it's one half base times height times the height again okay so let's not get confused there's lot of bees have lot of H's right so the the capital means the area of this base the area of this triangle the little means the length of the base so the base here in this triangle is either three or four okay three could be the base and four could be the height of the triangle kind of like this see three and four okay and then the height okay the overall prison is the ten that's what's separating the two triangles that you parallel congruent bases so if we put these values in we have one half three times four and then the overall height is ten if we multiply all those together we get 3 times 4 is 12 times 10 is 120 times 1/2 or divided by 2 is going to give you 60 units cubed so cubed means we're filling this up with like little ice cubes you know so to speak like that how many of those little cubes would fill up the inside of this container ok the next example we're going to talk about the volume of cylinder now just want to say if you're enjoying these videos go ahead and subscribe to the channel and I've got more videos like this coming for you and you can take check out some of my past videos but let's look at this last example cylinder ok same idea we're going to find the volume so it's the area of the base times the height the bases of circle what's the formula for area of circle it's PI squared right so and then times the height so the overall height we know is 10 we know what pi is 3.14 and then the radius is the distance from the center of the circle to point on the circle so they give us that that's 4 4 squared so remember you want to do the order of operations parentheses exponents multiplication right so 4 squared is 16 times 10 is 160 and we'll just leave pius pi so that'll give us an exact answer 160 PI units cubed we're filling this up with like little ice cubes is this glass okay so again hope you're enjoying the videos go ahead and comment below and let me know what you liked about the videos and maybe what could do better to improve the videos and look forward to seeing you in the future future videos I'll talk to you soon