# Mass of a sphere

1. Apr 4, 2016

### reminiscent

1. The problem statement, all variables and given/known data
Find the mass M of a sphere of radius a, if its mass density is proportional to the distance
from the center of the sphere.

2. Relevant equations
Triple integrals using spherical coordinates

3. The attempt at a solution
The only place where I am stuck is if the density is KpcosΦ or just Kp. So is it integrating KpcosΦp2sinΦ or Kp3sinΦ?

2. Apr 4, 2016

### Samy_A

Let me emphasize a part of the question: its mass density is proportional to the distance from the center of the sphere.

3. Apr 4, 2016

### Buzz Bloom

Hi reminiscent:

You only need to integrate with respect to r. What is the mass of a shell of thickness dr at radius r?

Regards,
Buzz

4. Apr 4, 2016

### princessp

can you guys please elaborate on this?

5. Apr 4, 2016

### HallsofIvy

Staff Emeritus
Samy_A's point is that the problem said that the mass is proportional to the distance to the center of the sphere. That distance is the variable $\rho$.

BuzzBloom's point is that, since the mass is given by $$\int_0^a\int_0^\pi\int_0^{2\pi} K\rho (\rho^2 sin(\theta) d\phi d\theta d\rho)= \int_0^a\int_0^\pi\int_0^{2\pi} K\rho^3 sin(\theta) d\phi d\theta d\rho$$

6. Apr 4, 2016

thanks :D