Here is how all these files work together.

To compute the volume of the hemisphere, enter the command window

vol = quad('areaHemisphere', -3, 3 )

This command calls the Matlab integration routine quad and integrates the function areaHemisphere from -3 to 3.

We next go to the torus.  (Problem 2)

The function that computes the area of the shell is areaShell().

To get the whole volume of the torus, we integrate the function areaShell from 1 to 3 with

vol = quad('areaShell', 1, 3 )

To find the volume from 1 to X we could use

X = 2 % or whatever value you want.
vol = quad('areaShell', 1, X )

This is put into the function volumeTorus, so you could also use

vol = volumeTorus(2) % or whatever value you want.

To find the value of t where the volume is 20, we first make the function volLess20,
(check what this function does) and then use fzero.  The command is 

t20 = fzero('volLess20', [ 1.2 , 2.9 ] )

The two values in the vector passed to fzero are such that volTorus(1.2) is less than
20 and volTorus(2.9) is greater than 20, so we know that t20 will be between these values.

We now consider slicing the torus the other way. (Problem 3)

We use the function that computes the area of the 'washer.'  This is the difference of
the area of the larger disk and the smaller disk.  This is the function areaSlice.

As before, we integrate with quad.  This is in the function volumeDisk.

To find the value of y where the volume is 20, we use fzero, as in

s20 = fzero('volDiskLess20', [0, .9] )

Again, the values in the vector are chosen so that volumeDisk(0) is less than 20 (it is 0)
and volumeDisk(.9) is greater than 20.