Ever Eaten A Square Pizza?

fraction of area occupied by the square pizza under the circular base is 2/pi whereas fraction of area occupied by the circular pizza inside the square base is pi/4. Clearly first is less then second.

*I don't know how to type in subscript, can someone enlighten me?

You have 2 cases, let $X$ be symbols of what we are looking for.

$A:$ Round pizza $X^{rp}$ in Square box $X^{sb}$

$B:$ Square pizza $X^{sp}$ in Round box $X^{rb}$

$A:$

Let the Sides of the Square box be:

$l^{sb}=2m$

Then the Area of the Square box will be:

$A^{sb}=(l^{sb})^2$

$A^{sb}=4m^{2}$

Then the Radius of the Round pizza will be:

$r^{rp}=(l^{sb})/2$

$r^{rp}=1m$

Then the Area of the Round pizza will be:

$A^{rp}=\pi (r^{rp})^2$

$A^{rp}=\pi m^2$

Then the Percentage of Area in case $A$ will be:

$Percentage - Of - Area^{case A}=[(A^{rp})/(A^{sb})] *100\%$

$Percentage - Of - Area^{case A}=[\pi /4] *100\%$

$Percentage - Of - Area^{case A}=78.54\%$

$B:$

Let $A^{sp}=A^{rp}$

Then:

$A^{sp}=\pi m^2$

Then the Sides of the Square pizza will be:

$l^{sp}=\sqrt\pi m$

Then the Radius of the Round box will be:

$r^{rb}=\sqrt{({\sqrt\pi}/2)^2+({\sqrt\pi}/2)^2}$

$r^{rb}=\sqrt{(\pi/4)+(\pi/4)}$

$r^{rb}=\sqrt{\pi/2} m$

Then the Area of the Round box will be:

$A^{rb}=\pi(r^{rb})^2$

$A^{rb}=\pi^2 /2 m^2$

Then the Percentage of Area in case $B$ will be:

$Percentage - Of - Area^{case B}=[(A^{sp})/(A^{rb})] *100\%$

$Percentage - Of - Area^{case B}=[2\pi /\pi^2] *100\%$

$Percentage - Of - Area^{case B}=[2 /\pi] *100\%$

$Percentage - Of - Area^{case B}=63.66\%$

Thus, Percentage of Area of Round pizza in Square box is more than the Percentage of Area of a Square pizza in a Round box.

The Answer of this question would be: $No.$

pi/4 > 2/pi, R.: "No"

(square in circle)2/pi < (circle in square)pi/4

The square pizza will cover less area i compression with respective circular pizza . If 'a' be the diameter of the pizza the corresponding diameter side of the box should be 'a'.