A solid has its circular base on the x-y plane, center at the origin and a radius of 0.5. Its height is determined by

z=cos⁡(x-0.25) sin⁡(y-0.9)+4

Picture the solid as a cylinder but the top of it is not flat, rather it is cut by the function expressed by the equation above

a. Create a mesh plot of the function from x = [-0.5,0.5] and y = [-0.5,0.5]. Note: This will plot the entire square area, not just the cylindrical solid
b. Find the volume of the solid using Monte Carlo Integration. You need to find the average height of the solid on the xy domain. You will then find the volume of a cylinder with a uniform height that has the same volume as the solid. We do not have an analytical solution for this problem so you must validate your solution by demonstrating convergence (include plot).