Use the cylindrical coordinate system to find the formulas f

Use the cylindrical coordinate system to find the formulas, for the circumference and area of a circle of radius a. Use Matlab to estimate the integrals by summations, this involves using Delta l and Delta A approximations to the dl and Delta A in the r, phi, z coordinate system, over the ranges of r and phi. Calculate the areas and circumference for a number of different radii, and use the Matlab command \"polyfit\" to verify the power of radius and the coefficient in the area and circumference formulas. Repeat this process for determining the formulas for area and volume of a sphere as a function of its radius. Use Delta S and Delta V approximations to the dS and dv in the R, theta, phi coordinate system, and sum, rather than integrate, over the ranges of R, theta, and phi.

Solution

[theta,rho] = cart2pol(x,y)
[theta,rho,z] = cart2pol(x,y,z).

[theta,rho] = cart2pol(x,y) transforms corresponding elements of the two-dimensional Cartesian coordinate arrays x and y into polar coordinates theta and rho.

[theta,rho,z] = cart2pol(x,y,z) transforms three-dimensional Cartesian coordinate arrays x, y, and z into cylindrical coordinates theta, rho, and z.
for generating sphere:
sphere
sphere(n)
sphere(ax,...)
[X,Y,Z] = sphere(...)

The sphere function generates the x-, y-, and z-coordinates of a unit sphere for use with surf and mesh.

sphere generates a sphere consisting of 20-by-20 faces.

sphere(n) draws a surf plot of an n-by-n sphere in the current figure.

sphere(ax,...) creates the sphere in the axes specified by ax instead of in the current axes. Specify ax as the first input argument.

[X,Y,Z] = sphere(...) returns the coordinates of the n-by-n sphere in three matrices that are (n+1)-by-(n+1) in size. You draw the sphere with surf(X,Y,Z) or mesh(X,Y,Z).