A woodworker has made four small airplanes and one large
airplane. All airplanes are
exactly the same shape, and all
are made from the same kind of
wood. The larger plane is twice
as large in every dimension as
one of the smaller airplanes. The planes are to be painted and then shipped as gifts.
a. The amount of paint required to paint the planes is directly proportional to the surface area. Will the amount of paint required for the single plane in Case A be greater than, less than, or equal to the total amount of paint required for all four planes in Case B?
b. The shipping cost of the planes is proportional to the weight, which is related directly to the volume. Will the weight of the single plane in Case A be greater than, less than, or the same as the total weight of all four planes in Case B? How much more or less than (if applicable)?