Rectangular Plate?

Question

A thin rectangular plate of uniform areal density σ = 2.73 kg/m2 has length of 37.0 cm and width of 24.0 cm. The lower left hand corner is located at the origin, (x,y)= (0,0) and the length is along the x-axis.

1) There is a circular hole of radius 7.00 cm with center at (x,y) = (12.50,10.00) cm in the plate. Calculate the mass of plate.

If I find the volume of the plate, I can find the mass, but how do I find the volume if no other dimensions are provided?

2)Calculate the x-coordinate of the center of mass of the plate.

Would an equation like this work?
X = (Xd*Vd - Xh*Vh) / (Vd-Vh)

where Xd = center of mass of the whole object (including
the cut circle)
Vd = surface area of the whole plate
Xh = center of mass of the cut circle ONLY
Vh = surface area of the cut circle ONLY

Thanks in advance for your help.

Answer 1

Look at the units, you don't need the thickness

m=2.7 kg/m^2 *0.37 m*0.24 m=0.24kg

For the second, you're intuition is basically correct.

(0.37/2*(2.73*0.37*0.24)-π0.07^2*2.73*0.12)/((2.73*0.37*0.24-π0.07^2*2.73)=
(0.0448-.005)(0.2424-.0424)=0.1986 m

Answer 2

The mass is going to have a thickness variable (like 4.5t kg) but when you work on the center of mass, the thickness will drop out.

Answer 3

excuse me, yet this isn't any longer particularly confusing. you're only being lazy. calculate the cm of the plate and hollow, and evaluate the whole mass as being at a point. then subtract.

Answer 4

You have the density as 2.73kg/cm² whereas density refers to volume not area.