Volume of a Cone using Calculus

Hey guys. Here's a problem which has been bothering me for sometime. Most of us know how to find the volume of a cone by the "Regular" calculus method. Taking it a series of infinitesimal disks and integrating.

But my question is this? Why take disks? There are so many different conic sections. Why not take it as a series of infinitesimal parabolic areas or if we need to find surface area, why not take it as a line revolving around the central axis?

Is my reasoning flawed, or is there a hurdle which prevents us from doing this through any other infinitesimals? I do apologize if my question was redundant. Thank you for any answers.

#Geometry #Calculus #Math

Easy Math Editor

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Comments

Well, it might be possible. But if we can do it with disks, why should we use another way? The one with disks is arguably the simplest method. Of course, finding another method that is completely unrelated might help for checking for errors, but basically it's not necessary to arrive at a conclusion.

I might not get your point correctly. If the above doesn't answer your question, can you elaborate?

Ivan Koswara - 7 years, 8 months ago

trying new method makes your conceprt clear of course you can rotate it and try finding it out

Vignesh Subramanian - 7 years, 8 months ago

Maybe this article might be of some help. $Volume = 2\pi\text{(Area of right angled triangle)}\cdot x_{C}$ . Where $x_C$ is the geometrical centroid (The point which is often referred to as the Center of Mass in Physics ).

Shaswata Roy - 7 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$