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GATE 2021 EC – Question 8

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is ________.

  1. $\frac\pi3$
  2. $\frac{2\pi}{3}$
  3. $\frac{3\pi}{2}$
  4. $3\pi$

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Correct answer: (A) $\frac\pi3$

Explanation

Each half is a right isosceles triangle with legs 1 and hypotenuse $\sqrt2$. Revolving about a leg (the short edge) gives a cone with height $h=1$ and base radius $r=1$, so $V=\frac13\pi r^2h=\frac{\pi}{3}$.