GATE | GATE CS 2018 | Question 5

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) πd
(B) πd2
(C) (1/4) πd2
(D) (1/2)πd

Answer: (D)

Explanation: circle-square

One important observation to solve 
the question :

Diagonal of Square = Diameter of Circle.

Let side of square be x. 

From Pythogorous theorem.
Diagonal = √(2*x*x)

We know area of square = x * x = d

Diameter = Diagonal =  √(2*d)

Radius = √(d/2)
Area of Circle = π * √(d/2) * √(d/2) = 1/2 * π * d

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