general aptitude gate 2018

Question

If ther area of square is  d , then what is  the area of circle that passes through diagonal of square  . having diagonal as its diameter

Comments

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

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i got same ans

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yes got same

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Yes i answered same

Answer 1

The side of square= ${\sqrt{d}}$

The diagonal by Pyathagoras Theorem is ${\sqrt{2d}}$ units long, which is diameter.

Radius = ${\sqrt{d/2}}$

Area= pi*${\sqrt{d/2}}$*${\sqrt{d/2}}$=${\Pi}$d/2

Answer 2

For the sake of completeness:

Aread of sqaure =  $d$

then, side of sqaure = $\sqrt(d)$

length of diagonal (using $a^2 + b^2 = c^2$), = $\sqrt(2d)$

as this is the diameter of the circle, radius of the circlet = $\sqrt(\frac{d}{2})$

Area of circle, using $\pi * r^2$ = $\pi * \frac{d}{2}$

Answer 3

Let side of the square is a
then a^2=d
now diagnol will  be square root (2a^2)
Now to find out the area of circle
formula will be  Pi. [1/2 ( square root (2a^2))]^2
which will give finally (Pi.d)/2