A woodworker has made tour small airplanes and one large airplane. All airplanes

Question

A woodworker has made tour small airplanes and one large airplane. All airplanes arc 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 planes. The planes are to be painted and then shipped as gifts. 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 (i) greater than, (ii) less than, or (iii) equal to the total amount of paint required for all four planes in Case B?

Explanation / Answer

Case A would require less paint than case B.
A bigger object when broken into smaller similar objects results in increaseof total surface area.
consider an example of sphere where Surface area =4 pi r2.
if the radius of the bigger object is R.then radius of smaller sphere would be (R3/4)-3.
now total surface area of smaller objects would be greater than the bigger one.
we apply the similar funda here

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