Cone's volume, not seeing a step posted elsewhere

  • Thread starter Damascus Road
  • Start date
  • Tags
    Volume
In summary, the conversation is about a question regarding the integral of a cone. The person asking the question is unsure why the x is squared and why there is an x in the formula. Another person, Damascus Road, responds by explaining that the cone is sliced into discs and provides the formula for the volume of a disc. The original poster then realizes that the formula is correct and thanks Damascus Road.
  • #1
Damascus Road
120
0
Hey all,

can you check out this site

http://www.mathisfunforum.com/viewtopic.php?pid=49738

In the very first line of the integral, I'm not sure why it's squared, or why the x is there. Can someone explain this?
Clearly, its correct because the correct answer is derived lol.

Thanks!
 
Physics news on Phys.org
  • #2
Damascus Road said:
I'm not sure why it's squared, or why the x is there.

Hi Damascus Road! :smile:

The cone is sliced into discs of thickness dx at height x.

So the radius of each disc is x/h times the base radius (r),

and the volume of the disc is that squared times π times dx.
 

FAQ: Cone's volume, not seeing a step posted elsewhere

What is the formula for calculating the volume of a cone?

The formula for calculating the volume of a cone is V = 1/3πr²h, where r is the radius of the base and h is the height of the cone.

Do I need to know the height of the cone to calculate its volume?

Yes, the height of the cone is a necessary component in the formula for calculating its volume.

Can I use the same formula for different types of cones?

Yes, as long as you have the radius and height of the cone, you can use the same formula to calculate its volume regardless of its shape or size.

How do I convert the volume of a cone from cubic units to another unit of measurement?

To convert the volume of a cone from cubic units to another unit of measurement, you can use conversion factors such as 1 cubic inch = 0.0005787 cubic feet or 1 cubic meter = 1000000 cubic centimeters.

Can I use the volume of a cone to find its surface area?

No, the volume and surface area of a cone are two different measurements and cannot be directly calculated from one another. However, you can use the volume to find the radius or height of the cone, which can then be used to calculate the surface area using a separate formula.

Similar threads

I Question about Integrals to Determine Volume vs Surface Area
Replies
5
Views
1K
B Having trouble deriving the volume of an elliptical ring toroid
Replies
4
Views
2K
Volume Inside a Sphere and Cone?
Replies
2
Views
2K
MHB Calculate volume of a solid rotating around the y-axis
Replies
1
Views
2K
MHB Calculate the volume of the space D
Replies
9
Views
2K
Deriving the volume and surface area of a cone
Replies
7
Views
8K
Volume between truncated cone and an inclined plane
Replies
3
Views
7K
Optimization problem - right circular cylinder inscribed in cone
Replies
9
Views
3K
MHB Find volume of solid generated (Calc 2)
Replies
3
Views
14K
I Surface of a cone by integration
Replies
8
Views
3K

Hot Threads

Recent Insights

Back
Top