Finding the area of a cone is just like finding the volume of a cylinder, you just have to keep in mind that it takes up a certain amount of space inside the cylinder. If you don't know what I mean, read more to find out!
ISAIAH LOPEZ
Ok. So... do you know how to calculate the volume of a rectangular prism? Probably. It's just length times width times height. And do you know how to calculate the volume of a cylinder? If you don't know it then check out my other widget called Volume With Pi. Ok, so moving on. To calculate the volume of a rectangular pyramid, it's actually the same formula as the volume of a rectangular prism or cube, with the exception of dividing the whole thing by three. If you know a bit about volume, you have probably heard that the formula for a rectangular pyramid is 1/3 l w h, or 1/3 base times height. Well what is actually going on there is whenever you multiply something by fraction with one in the numerator, it is that something over the denominator. For example 1/2 of 3 is 3/2 or 1/7 of 374 is 374/7. Of course you can simplify this as well, but you probably understand. Also, 1/3 (l w h) is the same thing as (l w h)/3.
Once you understand that you can pretty much figure out the volume of any three-dimensional shape with a slanted surface. Even a cone works in that way. You just need to know the volume of a cylinder, and to know that, you need to know the area of a circle. So the area of a circle is πr² or pi times the radius squared. The volume of a cylinder is just that times the height (h). To find the volume of a cone, you just need to do that same formula for a cylinder (πr²h), but divide the product by three (πr²h/3).
The last thing this article will cover is why you need to divide by three. It has to do with the way geometry works in a two-dimensional space. Two triangles of any type can fit into a rectangle of equal base and height. You might have to break it up into pieces but it will still fit. It works the same way with three-dimensional shapes and figures, except that it takes three pyramids to occupy a rectangular prism, and three cones to occupy a cylinder. It also goes on and on. 4 of whatever the 4-D Shape would be would fit into a hypercube, or tesseract, but that's a whole different lesson for another day. I hope this article allowed you to understand the concept volume for slanted 3-D shapes. Make sure to keep your brain sharp like a cone!