How Do You Calculate the Volume of a Cylinder Using Triple Integrals?

In summary, the conversation is about a cylinder volume problem where the volume V inside a cylinder is given by x^2 + y^2 = 4R^2 and z=(3x^2 + 2y^2)/R, with cartesian coordinates xyz and a constant R. The task is to write a triple integral using cylindrical coordinates for the volume V with 3 upper and 3 lower limits. The person has been struggling with this question for 3 days and is looking for help. They have made some attempts but are having trouble finding the correct limits. The conversation also clarifies that the radius is from 0 to R, not 0 to 4R^2.
  • #1
Bowenwww
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Cylinder volume problem Please Help!

Basically I've been attempting this question for at least 3 days now and it's driving me insane. The question goes like this - Consider the volume V inside a cylinder x^2 + y^2 = 4R^2 between z=(3x^2 + 2y^2)/R and the xy plane, xyz are cartesian and R is constant - Write down a triple integral using cylindrical co-ordinates for the volume V giving 3 upper and 3 lower limits




I first started by stating that r = 4R^2 The first limit (LHS to RHS) should surely be 0 to 2π the second should be from the origin to the radius i.e. 0 to 4R^2 and the third limit should be 0 to Z but I'm having a nightmare solving it or finding the right limits, any help would be greatly appreciated as I'm losing serious patience :( TIA.
 
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  • #2


What does your triple integral look like?

And by the way, the radius is r is from the origin 0 to R ( not 0 to 4R^2)
 
  • #3


256bits said:
What does your triple integral look like?

And by the way, the radius is r is from the origin 0 to R ( not 0 to 4R^2)

Gee. No response. Radius of circle is 2R.
 

FAQ: How Do You Calculate the Volume of a Cylinder Using Triple Integrals?

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

The formula for calculating the volume of a cylinder is V = πr2h, where V is the volume, π is approximately 3.14, r is the radius, and h is the height of the cylinder.

How do I find the radius of a cylinder if I know the volume?

To find the radius of a cylinder if you know the volume, you can rearrange the formula to solve for r. The formula would become r = √(V/πh), where r is the radius, V is the volume, π is approximately 3.14, and h is the height of the cylinder.

What units should I use for the measurements in the cylinder volume formula?

The measurements for the radius and height in the cylinder volume formula should be in the same unit (e.g. inches, centimeters, etc.). The resulting volume will then be in cubic units (e.g. cubic inches, cubic centimeters, etc.).

Can I use the cylinder volume formula for any type of cylinder?

Yes, the cylinder volume formula can be used for any type of cylinder, as long as you have the measurements for the radius and height. This includes right cylinders, oblique cylinders, and even irregular cylinders.

How accurate is the cylinder volume formula?

The cylinder volume formula is very accurate when used correctly. However, it is important to note that the formula assumes the cylinder has a perfectly circular base and a uniform height. If the cylinder is not perfectly symmetrical or has varying heights, the calculated volume may not be completely accurate.

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