What method to use to calculate volume

In summary, the difference between single variable calculus (specifically Solids of Revolution) and multivariable calculus (double and triple integrals) lies in their methods of finding volume. Multivariable calculus can be used to prove the volume identities in single variable, but if the object is a simple rotation in two dimensions, single variable methods are easier to use. However, they are just special cases of the multivariable method, which may require more effort to remember.
  • #1
thushanthan
32
0
Hi

Can anyone explain to me the difference between the following:

Single variable Calculus : Solids of Revolution

Multivariable : Double and Triple Integrals.

When I tried to connect these topics, I found the same answer : Volume.

My question is how to decide on the method to use? Thank you!
 
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  • #2


You can actually use multivariable calculus to prove the volume identities in single variable. If we don't have a simple rotation of a two-dimensional object, then we resort to multivariable, otherwise, it's simpler to use the single variable methods, thought it takes more effort to remember and they're just special cases of the multivariable method.
 
  • #3
thanks!
 

1. What is the most commonly used method to calculate volume?

The most commonly used method to calculate volume is by using the formula V = lwh, where l is the length, w is the width, and h is the height of the object.

2. How do I calculate volume using displacement?

To calculate volume using displacement, you need to fill a graduated cylinder or other container with a known volume of liquid, then submerge the object in the liquid. The difference in the liquid's volume before and after submerging the object is equal to the volume of the object.

3. Can I use Archimedes' principle to calculate volume?

Yes, Archimedes' principle can be used to calculate volume by measuring the amount of fluid displaced by the object. The volume of the displaced fluid is equal to the volume of the object.

4. Is there a specific method for calculating the volume of irregularly shaped objects?

Yes, the method for calculating the volume of irregularly shaped objects is by using the water displacement method or by dividing the object into smaller regular shapes and then calculating the volume of each shape separately.

5. How do I calculate the volume of a sphere?

The formula for calculating the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere. Alternatively, you can also use the water displacement method by submerging the sphere in a graduated cylinder and measuring the change in the volume of water.

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