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GATE 2018 CS – Question 3

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

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

  1. $\pi d$
  2. $\pi d^2$
  3. $\frac14\pi d^2$
  4. $\frac12\pi d$

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Correct answer: (D) $\frac12\pi d$

Explanation

The side of the square is $\sqrt d$, so its diagonal is $\sqrt{2d}$. This is the diameter of the circle, so the radius is $\frac{\sqrt{2d}}{2}$ and the area is $\pi\cdot\frac{2d}{4}=\frac12\pi d$.