Question

a circles diameter matches the side length of a square. What percent of the square's area is the circle's area?

Answer 1

78.5%

Explanation:

`\text{Let}\ s\ -\ \text{side length of a square. Therefore the diameter d = 2r has }\\\text{length d=s}\to 2r=s\to r=(s)/(2).\\r-\text{radius}\\\\\text{The formula of an area of a square:}\\\\A_(\square)=(side\ length)^2\\\\\text{Therefore:}\ A_(\square)=s^2.\\\\\text{The formula of an area of a circle:}\\\\A_O=\pi r^2\\\\\text{Substitute}\ r=(s)/(2):\\\\A_O=\pi\left((s)/(2)\right)^2=(s^2\pi)/(4)`

`\text{Calculate what fraction of the area of the square is the area of ​​the circle}\\\\(A_O)/(A_(\square))=((s^2\pi)/(4))/(s^2)=(s^2\pi)/(4)\cdot(1)/(s^2)\qquad\text{cancel}\ s^2\\\\(A_O)/(A_(\squera))=(\pi)/(4)\\\\\text{Convert to the percent:}\\\\(\pi)/(4)\cdot100\%=25\pi\%\\\\\pi\approx3.14\to25\pi\%\approx(25)(3.14)\%=78,5\%`