Consider a square sheet of a 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 _______.

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ELECTRONICE & COMMUNICATION 2021 GATE EXAM 

Question :Consider a square sheet of a 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. π3$\frac{\pi }{3}$
2. 2π3$\frac{2\pi }{3}$
3. 3π2$\frac{3\pi }{2}$
4. 3π$3\pi$

ANSWER : A

Given

The volume of a cone is 13πr2h,${\displaystyle \frac{1}{3}}\pi r^{2}h,$ where r$r$ denotes the radius of the base of the cone, and h$h$ denotes the height of the cone.

Here, h=r=1.$h=r=1.$

∴$\therefore$ The volume of cone =13πr2h=13π(1)2(1)=π3$={\displaystyle \frac{1}{3}}\pi r^{2}h={\displaystyle \frac{1}{3}}\pi (1{)}^2(1)={\displaystyle \frac{\pi }{3}}$ cubic units.