A lamina occupies the disk x squared space plus space y squared space less or equal than 4. Find the mass, if the density at any point is proportional to its distance from the origin, where the proportionality constant is 3.

Mass of Lamina is (K/3)

Centre of mass is (3/8, 3pi/16)

Step-by-step explanation:

Find explanation in the attachments

Ok so the end equation here is going to be VCy-VCo=
air space. So we need to find the volume of the cone and the volume of the cylinder.

Lets start with the volume of the cylinder since its easiest. The volume of a cylinder is Pi*r^2*h = Volume.
We already know that the radius is 5 and the height is 16 so lets plug them in and solve. 3.14*5^2*16=1,256

Now lets solve to find the volume of the cone. Now this ones a bit harder, the equation is: Pi*r^2*(h/3)= Volume.
The radius is 4 and the height is 12, so now just solve! 3.14*4^2*(12/3)=201

Now we just need to subtract the Volume of the cylinder from the volume of the cone. 1,256-201=1,055

If you have any questions just ask!