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

Answer:

78.5%

Step-by-step explanation:

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

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