- #1

Addez123

- 199

- 21

- Homework Statement
- Integrate 3 over a sphere with radius R.

- Relevant Equations
- Polar coordinates

##\iiint 3 dr d\rho d\phi##

The volume of a sphere is ##4\pi /3 r^3## so naturally the answer is ##4 \pi R^3##

But when I integrate I do:

##3 \iint r |_0^R d\rho d\phi##

##3R \int \rho |_0^{2\pi} d\phi##

##6R\pi * \phi |_0^\pi = 6R\pi^2##

What am I doing wrong?

The volume of a sphere is ##4\pi /3 r^3## so naturally the answer is ##4 \pi R^3##

But when I integrate I do:

##3 \iint r |_0^R d\rho d\phi##

##3R \int \rho |_0^{2\pi} d\phi##

##6R\pi * \phi |_0^\pi = 6R\pi^2##

What am I doing wrong?