From the question I gather the equation for the sphere(ball) is

What we're looking for is

where

So what are our bounds for theta, phi and p? Well, for P this is the value of the minimum point and maximum point. In this case, clearly the farthest point P is . But what is the shortest point/distance it can be? Well, in this case the origin! So,

From the question were are given our bounds of phi!

What about theta? Well, we are going 360 degress around the way! So our theta bounds become

Therefore,