Not quite. For the second part, you would need to do

Let me simplify the first part...

We can rewrite the equation

as

and

as

We can determine

two ways: by inspection or by evaluating the integral.

Since the semi-circle is symmetric about the y axis, we can determine that

. Now if you didn't see that, then we would evaluate the equation for

:

[Let me denote the radius of the circle as

instead of

]...

Note how we are using polar coordinates to evaluate the integral.

We now see that:

Are you still with me?

Now let's find

:

Thus, the centroid is

This answers your first question.

Now the second:

Using the theorem of Pappus, we can find this volume:

We know this to be true because the volume of a sphere is

I hope you can absorb all of this. If you have questions, feel free to ask!

--Chris