Define a function of the radius R which describes the volume in a ball of icecream of radius R which lies below the lip of the icecream cone. You may find it useful to refer to the formula for the volume of the cap of height H taken from a sphere of radius R. Notice that defining the function requires considering three three separate cases already mentioned. To deal with this you should use the piecewise command to define the function. (This is not available MapleVR3. In this case use the if ...then ...elif ...else ...fi; command. An alternate is to use the Heaviside fucntion). To begin, assume that that the angle formed at the tip of the cone is radians and that the height of the cone is 1 unit.
Plot the function you have defined and ask yourself if it agreees with
common sense. Here you should use the discont=true option to the
plot command so that you do not falsely connect the function at the
point where the definition changes.
Use the graph to estimate the largest amunt of icecream whic will be
contained below the lip of the cone.
(Experiment with plotting the
with and without the discont=true option.) To use this option invoke the plot command on a function f as follows:
solve the general icecream cone problem symbolically when the angle is radians.
Use plot3d to plot the volume as a function of both radius and
angle. Note that it is no lonegr possible to plot the function simply
as a function of R since the angle is not determined. What happens
if you do try to plot it?