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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 from solid cone. The volume of a resulting cone, in a cube units is _________.
- a)π/3
- b)2π/3
- c)3π/2
- d)3π
Correct 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 ...
Given : Square sheet of side 1 unit.
It is cut along the main diagonal to get two triangles
One of the cut triangle is revolved about its short edge to form solid cone
Hence, the correct option is (A).
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Consider a square sheet of side 1 unit. In the first step, it is cut ...
Given:
- Square sheet of side 1 unit
- Cut along the main diagonal to get two triangles
To find:
- Volume of the resulting cone
Solution:
Let's break down the problem into steps to find the volume of the resulting cone.
Step 1: Cutting the Square Sheet
When the square sheet is cut along the main diagonal, we obtain two congruent right-angled triangles.
Let's label the triangles as Triangle A and Triangle B.
Step 2: Forming the Cone
We revolve one of the cut triangles (Triangle A) about its shorter edge. This revolution creates a solid cone with the base formed by the longer edge of Triangle A.
Let's label the resulting cone as Cone C.
Step 3: Finding the Volume of Cone C
To find the volume of Cone C, we need to know its radius and height.
1. Radius of Cone C:
- The longer edge of Triangle A forms the base of Cone C.
- The length of this edge is equal to the length of a side of the original square sheet, which is 1 unit.
- Therefore, the radius of Cone C is 1/2 unit.
2. Height of Cone C:
- The height of Cone C is equal to the length of the shorter edge of Triangle A.
- Since Triangle A is a right-angled triangle, the length of the shorter edge can be found using the Pythagorean theorem.
- The hypotenuse of Triangle A (the main diagonal of the square sheet) has a length of 1 unit.
- The longer edge of Triangle A (the base of Cone C) has a length of 1 unit.
- Using the Pythagorean theorem, we can find the length of the shorter edge:
a² + b² = c²
a² + 1² = 1²
a² + 1 = 1
a² = 0
a = 0
- Therefore, the length of the shorter edge (and the height of Cone C) is 0 units.
Step 4: Calculating the Volume of Cone C
The volume of a cone can be calculated using the formula:
Volume = (1/3) * π * r² * h
Substituting the values we found:
Volume = (1/3) * π * (1/2)² * 0
Volume = 0
Conclusion:
The volume of the resulting cone, Cone C, is 0 cubic units.
Therefore, the correct answer is option 'A' (π/3).
- Square sheet of side 1 unit
- Cut along the main diagonal to get two triangles
To find:
- Volume of the resulting cone
Solution:
Let's break down the problem into steps to find the volume of the resulting cone.
Step 1: Cutting the Square Sheet
When the square sheet is cut along the main diagonal, we obtain two congruent right-angled triangles.
Let's label the triangles as Triangle A and Triangle B.
Step 2: Forming the Cone
We revolve one of the cut triangles (Triangle A) about its shorter edge. This revolution creates a solid cone with the base formed by the longer edge of Triangle A.
Let's label the resulting cone as Cone C.
Step 3: Finding the Volume of Cone C
To find the volume of Cone C, we need to know its radius and height.
1. Radius of Cone C:
- The longer edge of Triangle A forms the base of Cone C.
- The length of this edge is equal to the length of a side of the original square sheet, which is 1 unit.
- Therefore, the radius of Cone C is 1/2 unit.
2. Height of Cone C:
- The height of Cone C is equal to the length of the shorter edge of Triangle A.
- Since Triangle A is a right-angled triangle, the length of the shorter edge can be found using the Pythagorean theorem.
- The hypotenuse of Triangle A (the main diagonal of the square sheet) has a length of 1 unit.
- The longer edge of Triangle A (the base of Cone C) has a length of 1 unit.
- Using the Pythagorean theorem, we can find the length of the shorter edge:
a² + b² = c²
a² + 1² = 1²
a² + 1 = 1
a² = 0
a = 0
- Therefore, the length of the shorter edge (and the height of Cone C) is 0 units.
Step 4: Calculating the Volume of Cone C
The volume of a cone can be calculated using the formula:
Volume = (1/3) * π * r² * h
Substituting the values we found:
Volume = (1/3) * π * (1/2)² * 0
Volume = 0
Conclusion:
The volume of the resulting cone, Cone C, is 0 cubic units.
Therefore, the correct answer is option 'A' (π/3).
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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 from solid cone. The volume of a resulting cone, in a cube units is _________.a)π/3b)2π/3c)3π/2d)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 from solid cone. The volume of a resulting cone, in a cube units is _________.a)π/3b)2π/3c)3π/2d)3πCorrect answer is option 'A'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) 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 from solid cone. The volume of a resulting cone, in a cube units is _________.a)π/3b)2π/3c)3π/2d)3πCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 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 from solid cone. The volume of a resulting cone, in a cube units is _________.a)π/3b)2π/3c)3π/2d)3πCorrect answer is option 'A'. Can you explain this answer?.
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