Part1: The goal of this part is to find the work required to build a snowman. The snowman is
to be 6ft tall comprised of three large snowballs. The base of the snowman should be a
snowball with radius 1.5 ft. The midsection of the snowman is to be a snowball with radius 1
ft. Finally, the head of the snowman is a snowball with radius of 0.5 ft.
Step 1: Have Maple draw the 2-dimensional version of a snowman superimposed with
coordinate axes such that the bottom center of the snowman is at the point (0,0). Your output
should look similar to the picture in Figure 1 below. The equations you type in to draw the
snowman will become very important to the solution of the problem.
Figure 1
Figure 2
The Maple syntax using implicitplot that allows plotting of top view of snowman (Figure 2
above) is given below. You must modify this syntax to get the plot required in Figure 1:
>with(plots):
>implicitplot({x^2+y^2=1.5^2, x^2+y^2=1^2, x^2+y^2=.5^2}, x=-1.5..1.5, y=-1.5..1.5);
Step 2: Have Maple find the work required to build the snowman (Assume that the density of
snow is 25 pounds per cubic foot.) Hint: It may be easiest to calculate the work required to
build the bottom sphere, the mid-section, and head separately and sum the results at the end.
If you use fractions in your work, Maple will give exact results. To receive full credit: You
must give an explanation of how the problem is solved as if you were teaching someone else
how to do it.
Part 2: You have made a snowball with a radius of 3 ft. What would the radius of a second
snowball have to be so that if you put it on top of the first one, it would take the same amount
of work? As in Part 1, be sure to include a detailed explanation of your solution to the
problem. Hint: first sketch the finished result and find an implicit function for each snowball.