How to Calculate the Volume of a Cone

Video Transcript

"Hi, I'm Steve Jones and I'm going to explain how to calculate the volume of a cone. Now a cone of course is circular in base, coming to a point at the top and if this was a circular base, and the same all the way up like a prism then it would just be the area of the base times the perpendicular height. The perpendicular height here is H. Now I've set some values for these. I've set, pie as we know at three. Three point one, four, two but three will do. R, the radius of the base at two centimeters and H, the perpendicular height, perpendicular height from the center of the base to the top is six centimeters. So to do our calculation all we need to do is work out the area of the base, that's pie R squared, multiply it by the height, the perpendicular height H, and then multiply by the factor one third because not all of the space of the whole prism is taken up by the cone. Only one third of it. So let's try that calculation. So the volume of this cone will be equal to one third of pie, well pie we're using the value three, times R squared. R times R, that's two times two is four , times H. H being the perpendicular height. H is six. Now this is quite an easy calculation because of course one third times three is just one and this gives us a value of, four sixes, twenty-four. Now this is going to be centimeters cubed. Cubic centimeters, because volumes are measured in cubic centimeters, not square centimeters or centimeters. So that is how we can calculate the volume of a cone."