Which occupies a larger percentage of the area compared to the figure containing it: a circle inscribed in a square or a square inscribed in a circle? Assume that the inscribed figures are tangent to the outside figures. Explain.
Which occupies a larger percentage of the area compared to the figure containing it: a circle inscribed in a square or a square inscribed in a circle? Assume that the inscribed figures are tangent to the outside figures. Explain.
Hi
The area of a square with length a is $\displaystyle A_{square} = a^2$
The diameter of the circle tangent to the square is a. Its area is $\displaystyle A_{circle} = \pi\frac{a^2}{4}$
The ratio of the 2 areas is $\displaystyle \frac{A_{circle}}{A_{square}} = \frac{\pi}{4} = 78.5 $%