How to Determine the Volume of a Conical Solid

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Determining the value of a conical solid will require you to think of the Pi R squared equation. Determine the value of a conical solid with help from an experienced mathematics educator in this free video clip.

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Video Transcript

Hi, my name is Marija, and today I'm going to show you how to determine the volume of a conical solid. So the first thing you need is a formula which is that the volume is one third Pi R squared times the height. So if we have a conical solid which is also just known as a cone, we're going to need to have all these dimensions. So the R stands for your radius which is the distance from the center of the circle of the cone to the end of the circle so let's say that is given as 3. You are also going to need the height and when we talk about height, we're not talking about this height here which is your slant height we are talking about the altitude. Okay so the altitude is going to be dropped from the top of the cone down to the circle to create a 90 degree angle. So if we are given the height as let's say 5 now we have the two dimensions that we need and we can substitute them into the formula. So we can say that the volume is equal to 1/3 times Pi, the radius squared. So my radius was 3 and 3 squared is 9 and my height was 5 so now I can simplify and I have volume equals 1/3. I'm going to switch these places 9 times 5 is 45 Pi and we can keep simplifying, 1/3 of 45 we're going to just do 45/3 Pi and then it depends on what your instructions were if you were asked to leave it in terms of Pi you can just leave it like that. If you were asked to use 3.14 as an approximation of Pi then you can go ahead and put that in your calculator and simplify.

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