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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)
    π/3
  • b)
    2π/3
  • c)
    3π/3
  • d)
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Consider a square sheet of side 1 unit. In the first step, it is cut a...
Concept:
The volume of the solid cone 
Calculation:
Given:
A square sheet of side 1 unit is cut along the diagonal.
Now the triangle is revolved along its shortest length to form a solid cone 

 
where R = 1 unit, H = 1 unit.
The required volume of the resulting cone is:
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Most Upvoted Answer
Consider a square sheet of side 1 unit. In the first step, it is cut a...
Understanding the Problem
To find the volume of the cone formed by revolving one of the triangles, we first need to analyze the shape and dimensions of the triangles.
Step 1: Triangle Dimensions
- The square has a side length of 1 unit.
- Cutting it along the main diagonal divides the square into two right-angled triangles.
- Each triangle has a base and height of 1 unit.
Step 2: Selecting the Triangle
- We can choose either of the two triangles; the result will be the same.
- For the purpose of this explanation, let's select the triangle with vertices at (0, 0), (1, 0), and (0, 1).
Step 3: Revolving the Triangle
- When we revolve this triangle about its short edge (the edge along the y-axis, from (0, 0) to (0, 1)), we create a cone.
- The height of the cone is the length of the edge we are revolving around, which is 1 unit.
- The radius of the cone is the length of the base of the triangle, which is also 1 unit.
Step 4: Volume of the Cone
- The formula for the volume of a cone is given by:
Volume = (1/3) * π * r^2 * h
- Substituting the values:
- r = 1 unit (radius)
- h = 1 unit (height)
- Thus, the volume becomes:
Volume = (1/3) * π * (1^2) * 1 = (1/3) * π = π/3 cubic units.
Final Answer
The volume of the resulting cone is π/3 cubic units, which corresponds to option 'A'.
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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)π/3b)2π/3c)3π/3d)3πCorrect answer is option 'A'. Can you explain this answer?
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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)π/3b)2π/3c)3π/3d)3πCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about 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)π/3b)2π/3c)3π/3d)3πCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)π/3b)2π/3c)3π/3d)3πCorrect answer is option 'A'. Can you explain this answer?.
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