4 25 Video Notes Volume of Prisms and Cylinders

all right let's talk about volume of prisms in cylinders my opinion volume is easier than surface area and for the most part that's why like to save it till the end let's go ahead and talk about this volume is the amount of space enclosed in the interior of 3d figure or an object so we're now it's filling up the the prism it's filling up the cylinder it's let's say filling it up with water okay that's what volume is you fill it with sand how much is in there we are going to be going into third dimension now okay so we will be using our units cubed so first of all the formula the formula for volume of any prism is big little we've already discussed big is area of the base is going to be that height connecting the two bases together first one here we're going to see all rectangles so that tells us we have rectangular prism all right and so now we're going to we don't need to find big anymore all we need is big and little so big the base we'll go ahead and use the shaded area as our base the base of rectangle is base times height so we're just going to multiply the two numbers together and big will come out to 48. your height is going to be that connection grab the right hand here it's going to be that connection between the two bases so right here this is going to be your height so we use our formula big little i'm just going to go ahead and plug in right here big would be 48 and your height of the prism is going to be 2. we multiply these together we are going to get 96 and we don't have units listed so we'll just put units we are now cubed we're going three dimensions now okay in reality what's going to end up happening with rectangular prism only with volume you simply just multiply the three numbers together because look what we did we did 8 times six and then we multiplied it by the two this only works with rectangular prism though right next see triangle know i'm doing prisms see bunch of those rectangles that tell me i've got prism and see triangle so we're gonna have triangular prism so again we need to remember that our base is going to be that triangle so that's what we're finding big right that's what we need to use so right here this is our base so to find the area big area of base we need our base times height divided by two okay so we take look at our rectangle we have our base of twelve we need to find the height so we're going to go to the side and we're going to say okay let's use this back one to find the height here we draw this triangle off we just kind of look at this triangle right here all right we're looking for height we have this leg over here because we know 12 we split it in half this is 6. so we're going to have pythagorean theorem of our height squared put it over here to the side we have our height squared plus the other leg of 6 squared is equal to the hypotenuse 10 squared and encourage you to pause this work it out i'm going to pause it in just second you're going to have all the work and the answer please pause it now so we should have found the height of the triangle not the prism the triangle to be eight so plugged it into the picture and plugged it over here in that same color okay once we have solved for big we are done with that eight throw it away ignore it we are no longer using that eight right when we solve for big as long as my math is correct we're going to wind up with 48 weirdly enough the same area of the base and last one so now we're going to plug in for our our formula area the base times the height remember your height connects your two bases together so it's going to be the pathway from one triangle to the next okay so again that for right here the base we're done with it we're finished with it completely ignore it okay the in our volume is going to be this 4 right here so we'll plug in big 48 times our height of the prism 4. we should come up with 192 units cubed again three dimensions now next am seeing here my base we're not sitting on the base but we have our two parallel sides the rectangles are our lateral faces so our base right here is hexagon so we have hexagonal prism to make this little bit easier for you we went ahead and gave you big okay and we just need to remember that your height is going to be what's connecting the two hexagons together okay so we have big 93.5 times that height that connects the two bases two hexagons together twelve when we multiplies again hoping that my original math and my answer key is correct 1122 units cubed it's very important to write these units cubed so we're seeing volume is three dimensional now next we have trapezoid we're very very lucky and we were given the big again but because our base is going to be this trapezoid doesn't matter if it's sitting on it or not we're looking for prisms we're looking for what's not the rectangle unless it's rectangular prism so this right here is our base and since it is trapezoid that fun word trapezoidal prism so they gave us big we remember that the height is going to be the path that connects or the edge we should have our vocabulary that connects the two trapezoids together okay how do get from one trapezoid to the other by taking the height of 10. so here big at 36 times the height of 10 easy to do in your head guys the rules of multiplying by 10. take the number 36 add that 0 onto it so we have 360 units again cubed with that three all right let's take look at the cylinders some nice and easy cylinders are your cylinders formula again volume same thing it's good so now we're filling up the cylinders think about how much is in can of soup okay that's what that liquid that's what the volume is here your volume is going to be equal to pi squared we're taking the area of the base and we're multiplying by the height okay so we have to stack all those circles together to get all the way up filling up that volume so we'll take look at our problem here and see that we have the radius that's given to us three my height right here from base to base six so we plug in our volume is going to equal pi times our radius squared three squared times the height of six we're going to round to the nearest tenth like we've been doing with these okay and when we plug this in and encourage you whether it's before or after put the answer plug it in yourself do not use 3.14 you need to use the pi button we should come up with 169.6 the units are inches so we have inches cubed next we're given our radius right here of 8 our height of 12. so let's plug in we have pi times our radius squared times our height of 12. plug it in on your own write this before after make sure that you're getting 2412.7 inches inches cubed last one do not say the height is 15 because it is not okay lot of students see that up and down like okay that's my no that is in the circle this is your diameter so your diameter is 15. so we're going to write in our radius as half of that which would be 7.5 then i'm going to scratch off the diameter so don't accidentally use it and fill in my radius of sorry 7.5 your height connects circle to circle even though it's laying down your height is still the same from your head to your feet even when you lay down 18. we'll fill in we got pi times your radius squared times the height from circle to circle yeah making sure that you're doing this on your own and seeing what we have in the end 3180.9 we have millimeters so we have millimeters cubed and that's volume