GATE EC 2021 Set 1 — Question 8
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General Aptitude → Quantitative Aptitude → Mensuration & Geometry
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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
Correct answer
(A) (π)/(3)
Solution
1.Understand the initial shape: We start with a square sheet of side 1 unit.
2.First cut: The square is cut along its main diagonal. This divides the square into two congruent right-angled isosceles triangles. Each triangle has two sides of length 1 (the sides of the original square) and a hypotenuse of length (the diagonal of the square).
3.Second step - Revolution: One of these triangles is revolved about its short edge. In a right-angled isosceles triangle with sides 1, 1, , the short edges are the two sides of length 1. Let's choose one of these sides as the axis of revolution.
4.Forming a cone: When a right-angled triangle is revolved about one of its legs (short edges), it forms a cone. In this case:
- The radius () of the base of the cone will be the length of the other leg, which is 1 unit.
- The height () of the cone will be the length of the leg about which it is revolved, which is also 1 unit.
Substituting and :
cubic units.The final answer is
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