12 4 A Volume of Prisms and Cylinders

welcome to video 12 for volume of prisms and cylinders we have whole bunch of formulas to go over so let's get started first the volume of right rectangular prism as shown here is simply the area of the base times the height now the value of any prism does not have to be rectangular or right is also the volume or I'm sorry the area of the base times the height so notice I've got the stack of index cards the volume is simply all the index cards if were to slide the index cards like such it has the same base area in the same height so it's going to have the same value all the cross-sectional areas are the same that rectangle so in general the volume of any prism is the area of the base times the height and that comes from capillaries principle the volume of cylinder is also the area of the base times the height cross section let's go over what cross section is you might recall from algebra two conic sections we have cone and we dealt with some cross sections first if we cut the cone parallel to the base we obtain circle if we cut the cone at an angle such as this we obtain an ellipse if we cut the cone such that it's parallel to one of the edges so I'm going to cut it here parallel to this edge we get parabola the hyperbola is too difficult for me to do it's if you cut both top and bottom in this book for cross-sections we really talk about cutting always parallel to base so let's suppose had log like this and took my saw and cut it that would be the cross section if had hexagonal prism like this and took my saw and cut it that would be the cross-section again getting back to another type of example about an egg shaped like this and cut it that would be the cross-section obtained there so the cross-section in our book we're going to talk about it's the figure obtained when you cut salad parallel to the base so our book is going to use certain symbol and for cross sectional area our book uses with slash strip so based on all of that the value of prism or cylinder based on cross sectional area is simply the cross-sectional area times the height so this is kind of like the area of the base and as one more example here are two triangular prisms they have the same height and they have the same cross section so they won't have the same volume the volume is simply the area of the cross section times the height or in this case the air the base times height there you have it little bit of vocabulary on cross section and some volume formulas for various salads