==============================================================================
	areaSlice.m 
==============================================================================
%
% Computes the area of a slice of the torus parallel to the x-axis 
% taken at height y.
%
function a = areaSlice(y)

radiusOuter = 2 + sqrt(1 - y.^2); % radius of outer disk
radiusInner = 2 - sqrt(1 - y.^2); % radius of inner disk

% area = area of outer disk - area of inner disk
a = pi*(radiusOuter.^2 - radiusInner.^2);


==============================================================================
	volumeDisk.m 
==============================================================================
%
% Computes the volume of the solid obtained by slicing the torus
%      (x - 2)^2 + y^2 =1
% parallel to the x-axis at t and -t.
%
function vol = volumeDisk(t)

% take the volume from 0 to t and double it to get the volume from 
% -t to t
vol = 2 * quad('areaSlice', 0, t);


==============================================================================
	volDiskLess20.m 
==============================================================================
%
% Computes (the volume of the solid obtained by slicing the torus 
% parallel to the x-axis at t and -t) - 20.
%
% It's necessary to do this to use the function with Matlab's fzero 
% function (which assumes equations are set up in standard form: 
% f(x) = 0).
%
function vol = volDiskLess20(t)
vol = volumeDisk(t) - 20;