GATE ECE 2021 | GA | Question: 8

Question

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 ____________

• A. $\frac{\pi }{3}$
• B. $\frac{2\pi }{3}$
• C. $\frac{3\pi }{2}$
• D. $3\pi$

Answer 1

Given that: 

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

Here, $h = r = 1.$

$\therefore$ The volume of cone $ =  \dfrac {1} {3} \pi r ^{ 2 } h = \dfrac{1}{3} \pi (1)^{2} (1) = \dfrac{\pi}{3}$ cubic units.

So, the correct answer is $(A).$

Comments

Thanks @Prateek pallaw. Now it’s clear :)

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@Prateek pallaw, nice observation, i was not able to see the structure, but your approach made it visible, thanks a lot.

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one of the cut triangles is revolved about its short edge to form a solid cone.

The term "solid" might be confusing in this context. It could give the impression that a tangible cone has been formed through paper folding, similar to what can be achieved with a semicircle. However, the cone in question is conceptual; the triangle serves to outline its solid shape, should it materialize. 

P.S.: By using line AB as an axis of rotation and spinning the triangle rapidly around it, one could visualize the cone shape being described.