Find the Volume of Cones using Integral Calculus
Hi friends! I will show you how to find the volume of cones by using integral calculus!
The formula for the volume of any shape is the definite integral from one end of the shape (let's call it "a") to the other end of the shape (let's call this "b"). So the integral is from a to b of the area of the cross-section (If you cut or slice the shape, you find the area of the open surface) and then dx. We are trying to find the volume of the cone.
Here, the area of the cross-section of the cone is the circle! The area of a circle is pi times the radius squared. From the figure shown of the cone, you can take the height of the cross-section "y" divided by the total height "h". Set this equal to the radius of the circle "x" divided by the total radius "r". This is the proportional ratio/fraction method. You solve x in terms of y to get the area of the cross-section and substitute it into the definite integral volume formula!
In the next video, I will show you how to find the volume of a square pyramid using integration.
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