Question

If the perimeter of a square is equal to the perimeter of circle, then the rationof the area of the circle to that of the square is :

• A. ∏ : 1
• B. ∏ : 2
• C. 1 : ∏
• D. 4 : ∏

Answer 1

Answer:

D. 4 : ∏

$P_s=P_c$

$4a=2\pi r$

$a=\frac{\pi r}{2}$

$A_c=A_s$

$\pi r^2: a^2$

$\pi r^2:(\frac{\pi r}{2})^2$

$\pi r^2:\frac{\pi ^2r^2}{2^2}$

$4:\frac{\pi ^2r^2}{\pi r^2}$

$=4: \pi$