Find the average distance from the origin to the points

(1) in the ball \(\displaystyle B(0,a) \subset \Re^2\)

(2) in the ball \(\displaystyle B(0,a) \subset \Re^3\)

I need help setting up the problem. I'm not sure where to begin here.

EDIT: For (1), I worked backwards from the answer, \(\displaystyle \frac{2}{3}a\), to find a setup for the problem, but I'm not sure if I understand the meaning of the setup:

\(\displaystyle Ave. dist = \frac{1}{Volume(ball)}\int_{\theta=0}^{2\pi}\int_{r=0}^{a}{r*r dr d\theta}\)

Since I'm using polar coordinates, r is the Jacobian. And since I am finding the average distance from the origin to all the points in the ball, I want to add up all of those distances, r, in the integral and then divide by the volume of the ball. Does that explain that the setup?

For part (2), should I be using the same approach, but in spherical coordinates?

That is: \(\displaystyle Ave. dist = \frac{1}{Volume(ball)}\int_{\theta=0}^{2\pi}\int_{\phi=0}^{\pi}\int_{\rho=0}^{a}{\rho*{\rho}^2 \sin\phi d\rho d\phi d\theta}\)

(1) in the ball \(\displaystyle B(0,a) \subset \Re^2\)

(2) in the ball \(\displaystyle B(0,a) \subset \Re^3\)

I need help setting up the problem. I'm not sure where to begin here.

EDIT: For (1), I worked backwards from the answer, \(\displaystyle \frac{2}{3}a\), to find a setup for the problem, but I'm not sure if I understand the meaning of the setup:

\(\displaystyle Ave. dist = \frac{1}{Volume(ball)}\int_{\theta=0}^{2\pi}\int_{r=0}^{a}{r*r dr d\theta}\)

Since I'm using polar coordinates, r is the Jacobian. And since I am finding the average distance from the origin to all the points in the ball, I want to add up all of those distances, r, in the integral and then divide by the volume of the ball. Does that explain that the setup?

For part (2), should I be using the same approach, but in spherical coordinates?

That is: \(\displaystyle Ave. dist = \frac{1}{Volume(ball)}\int_{\theta=0}^{2\pi}\int_{\phi=0}^{\pi}\int_{\rho=0}^{a}{\rho*{\rho}^2 \sin\phi d\rho d\phi d\theta}\)

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