  # Will square pizza cover more percentage of area in box with circular base than circular pizza in box with square base?

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Usually, pizzas are circular and they come in boxes with a square base. The circular pizza covers some percentage of area of the square base of the box. Let's say someone makes a square pizza and puts it in a box with a circular base. Will the square pizza cover more percentage of area in the box with circular base than the circular pizza in the box with square base ?

Assume that both the pizzas fit perfectly inside their respective boxes. posted May 31, 2016

+1 vote

A circle in a square consumes more percentage of the area of the square ie., only 21.46% of the area is wasted.
On the other hand Square in circle wastes more area ie., 36.33% For the circle in the square case to find the area that is wasted by the circle in the square in percentage we can use the following method

((s^2-πr^2)/s^2)*100
=(1 - (πr^2/s^2)) *100 ------ 1
but here
r=s/2
s=2r
s^2=4r^2

so 1 becomes

(1-(π/4))*100
=21.46%

Similarly in the case of the square inside the circle we end up with the equation

(1 - (s^2/πr^2))*100 ------ 2
but here
2r=(√2)s
or
s^2=2r^2
so 2 becomes

(1 - (2/π))*100
=36.33%

So we can conclude that the circular pizza consumes more percentage area of the square box it is in than the vice versa case. answer Jun 4, 2016

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