Volume of Sphere: Find Integral Solution

In summary, the conversation discussed the formula for finding the volume of a sphere, which is V = (4/3)πr³. An integral solution in this context would mean finding the volume as a whole number without any decimals or fractions. Integration can be used to find the volume of a sphere by integrating the formula with respect to r. The volume of a sphere cannot be negative as it represents the amount of space inside the sphere. Real-life applications of finding the volume of a sphere include architecture, engineering, and science.
  • #1
cad2blender
6
0
Find the volume of the sphere:

f(x,y,z)=e^(x^2+y^2+z^2) over x^2+y^2+z^2≤9 using spherical coordinates

After working trough I get this enormous number 228965, when I know its 113.097 using the simple volume formula for a sphere. I think I am having trouble with the integration of e^(rho^2)*rho... Any tips guys?
 
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  • #2
Integration by parts!
 
  • #3
You might have better luck with the substitution u=rho2
 
  • #4
Which is of course correct. Apologies for my confusion.
 

1. What is the formula for finding the volume of a sphere?

The formula for finding the volume of a sphere is V = (4/3)πr³, where V is the volume and r is the radius of the sphere.

2. What is an integral solution?

An integral solution is a solution that is a whole number and not a fraction or decimal. In the context of finding the volume of a sphere, an integral solution would mean finding the volume as a whole number without any decimals or fractions.

3. How do you use integration to find the volume of a sphere?

To use integration to find the volume of a sphere, you would integrate the formula V = (4/3)πr³ with respect to r, from 0 to the given radius of the sphere. This would give you an equation in terms of r, which you can then solve for the volume.

4. Can the volume of a sphere be negative?

No, the volume of a sphere cannot be negative. The volume of a sphere is a measure of the amount of space inside the sphere, and space cannot have a negative value.

5. What are some real-life applications of finding the volume of a sphere?

Finding the volume of a sphere has many real-life applications, such as in architecture and construction for determining the volume of domes or curved structures. It is also used in engineering for calculating the volume of pipes or tanks. In science, the volume of a sphere is used to measure the volume of cells or particles. It is also important in mathematics for solving various geometric problems.

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