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

I am not able to get how it is revolved to get the cone. which side on the circumference..??

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imagin ABC  triangle and it revolves(rotates) around the AB axis to create a conical structure.

we do not have to join two edges here we just have to rotate it around the AB axis.

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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.