What Is the Volume of a Cylinder?

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The volume of a cylinder can be calculated by using the formula for the area of a circle multiplied by the height of the cylinder, expressed as pi R squared H. Calculate the volume of a cylindrical shape with instructions from a college-level math teacher in this free video on geometry.

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Video Transcript

So what is the volume of a cylinder? Hi, I'm Jimmy Chang, I've been teaching collegial mathematics for 9 years. And the volume of a cylinder, which is in the shape of a can most of the time, is, follows one very simple formula here, and here it is. The volume is equal to pie R squared H. Now if the pie R square looks familiar is because it's the area of a circle. And if you think about it in a cylinder that makes sense, because a cylinder actually has circular parts, the H refers to the height of the cylinder. So if you want to find the volume you need to know two things, one, how tall the cylinder is, and two, what the radius is. So here's a brief demonstration. Suppose you know that the radius of the cylinder is 5 feet, and you know that the height is 8 feet. Now because it is volume, you're talking about a 3 dimensional figure, your final answer in volume is going to be in cubic units, or in this case cubic feet. But once you have that established you will just plug everything in. So here we go. You have V equals to pie, times your R, your radius is 5 feet, so you have 5, always include the unit so you have the correct cubic units at the end, times the height, which is 8 feet, so you have pie, now 5 squared is 25, feet squared is feet squared times 8 feet. All it takes now is to multiply these numbers and these feet and you're done. You have pie times, 25 times 8, calculator or in your mind is going to be 200, and feet squared times feet is going to be feet cubed, or cubic feet, which is what you're looking for. So as a result the exact value of this particular cylinder would be 200 pie cubic feet. But if you want to find a decimal approximation you could either plug in the exact value for pie or as exact as a guess or the approximate value, which is 3.14, and you'll get a decimal representation of the volume of the cylinder. So my name is Jimmy Chang, and that's an example as to finding the volume of a cylinder.

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