How Is the Center of Mass Calculated for a Plate with a Circular Hole?

[djgh]

Homework Statement

A thin rectangular plate of uniform areal density σ = 3.06 kg/m2 has length of 37.0 cm and width of 25.0 cm. The lower left hand corner is located at the origin, (x,y)= (0,0) and the length is along the x-axis.

There is a circular hole of radius 6.50 cm with center at (x,y) = (12.50,10.50) cm in the plate. Calculate the mass of plate.

Homework Equations

The Attempt at a Solution

I need to:

Calculate the distance of the plate's CM from the origin.

I've calculated the x-coordinate of the center of mass with the equation:

x= [ ((L/2)*(l*w)) - ((2r)*pi*r^2) ] / [ (l*w) - (pi*r^2) ]

basically x= (x-component center of mass of rectangle)*area - (center of mass of circle)*area divided by total area with L = 0.37m (length of rectangular plate), l*w= area of plate, r= 0.65m, radius of circle cut out of plate. This comes out to be 0.194m and I know is correct.

However, I use the same equation, but replacing L with H, the height of the rectangle or 0.25m to find the y component, which I've calculated to be 0.124m. Then when I find that I used Pythagorean theorem or sqrt(x^2 + y^2) to find distance from origin to center of mass but I get a wrong answer, or answer that is supposedly wrong, which I calculate to be 0.230m. I think I'm doing it correctly, but supposedly I'm wrong, any ideas?

EDIT: SOLVED

Homework Statement

Homework Equations

The Attempt at a Solution

 

[Delphi51]

The method looks good. I got .195 for the x and .0555 for the y when I ran it through.

 

[djgh]

nevermind, figured out what was wrong