Question

The area of a square is d. What is the area of the circle which has the diagonal of the square as its diameter?

• A.
  $\pi d$
• B.
  $\pi d^2$
• C.
  $\frac{1}{4}\pi d^2$
• D.
  $\frac{1}{2}\pi d$

Answer 1

The correct option is D

$\frac{1}{2}\pi d$


$Areaofsquare=d$

$Sideonesideofsquare=\sqrt{d}$

$Diagonalofsquare=\sqrt{d+d}=\sqrt{2d}$

$Areaofcircle=\pi r^2$

$=\pi {\left(\frac{\sqrt{2d}}{2}\right)}^2$

$=\pi \frac{d}{2}$

$=\frac{1}{2}\pi d$