The 'Lenny Conundrum' authors, in Round 238, wrote:A Pteri with a light appetite could not finish his Rainbow Melt Pizza. In fact, he could only eat exactly half of it.
If the diameter of the pizza was 50cm, and it was a perfect semicircle, what is the area of the smallest square box, in square centimetres, that could contain the half pizza?
There is an unstated assumption, I think. (This assumption often arises, unclarified, in this sort of elementary-math questions.) We can find the area of the half-circle with diameter 50 (that is, half of the circle with radius 25), without difficulty. But--
Do we assume that we need a square that holds exactly that area, or do we work with the messier but more-realistic assumption that we want the pizza slices to remain palatable?
If we deal with the "ideal" (non-realistic) version, we would find the area of the half-circle (being (1/2)(pi)(25^2) cm^2), and that would be the area of the "smallest box" needed to contain the pizza. But this would work only if the pizza were rectangular pieces, or were pureéd to fill the box exactly.
In "real life", we'd want the pieces to remain whole. We might pull the pieces (generally four, in a half-pizza) apart and arrange them to fit more compactly in the given space, but there would, of necessity, be some open space in the box.
(Think about any pizza you've ever had delivered: It probably just fit the box, with the crust touching the middles of the four sides of the box, but the corners of the box were empty, because the circle didn't reach that far. We're dealing with something similar here.)
Since we don't know which assumption we are expected make, there is probably no way to know, before this Round closes next week, what the "correct" answer is meant to be.
Eliz.
