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A wire of diameter 3mm is wound about a cylinder whose height is 12cm and radius 5cm so as to cover the curved surface completely. Then the length of the wire is?
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A wire of diameter 3mm is wound about a cylinder whose height is 12cm ...
Understanding the Problem
To determine the length of the wire used to cover the curved surface of the cylinder, we need to analyze the dimensions and the method of winding.
Dimensions of the Cylinder
- Height of the cylinder (h) = 12 cm
- Radius of the cylinder (r) = 5 cm
Diameter of the Wire
- Diameter of the wire = 3 mm = 0.3 cm
- Radius of the wire (r_wire) = 0.15 cm
Calculating the Number of Turns
1. Height Coverage: Each turn of the wire will cover a height equivalent to the diameter of the wire:
- Height covered per turn = diameter of the wire = 0.3 cm
2. Total Number of Turns: To find the total number of turns (n), divide the height of the cylinder by the height covered per turn:
- n = Height of the cylinder / Height covered per turn
- n = 12 cm / 0.3 cm = 40 turns
Calculating the Circumference of the Cylinder
- The circumference (C) of the base of the cylinder is given by:
- C = 2 * π * radius
- C = 2 * π * 5 cm = 10π cm
Finding the Total Length of the Wire
- Total Length of the Wire (L) = Number of turns * Circumference
- L = 40 turns * 10π cm
- L = 400π cm
Final Calculation
- Approximating π as 3.14:
- L ≈ 400 * 3.14 cm = 1256 cm
Conclusion
The total length of the wire required to cover the curved surface of the cylinder completely is approximately 1256 cm.
To determine the length of the wire used to cover the curved surface of the cylinder, we need to analyze the dimensions and the method of winding.
Dimensions of the Cylinder
- Height of the cylinder (h) = 12 cm
- Radius of the cylinder (r) = 5 cm
Diameter of the Wire
- Diameter of the wire = 3 mm = 0.3 cm
- Radius of the wire (r_wire) = 0.15 cm
Calculating the Number of Turns
1. Height Coverage: Each turn of the wire will cover a height equivalent to the diameter of the wire:
- Height covered per turn = diameter of the wire = 0.3 cm
2. Total Number of Turns: To find the total number of turns (n), divide the height of the cylinder by the height covered per turn:
- n = Height of the cylinder / Height covered per turn
- n = 12 cm / 0.3 cm = 40 turns
Calculating the Circumference of the Cylinder
- The circumference (C) of the base of the cylinder is given by:
- C = 2 * π * radius
- C = 2 * π * 5 cm = 10π cm
Finding the Total Length of the Wire
- Total Length of the Wire (L) = Number of turns * Circumference
- L = 40 turns * 10π cm
- L = 400π cm
Final Calculation
- Approximating π as 3.14:
- L ≈ 400 * 3.14 cm = 1256 cm
Conclusion
The total length of the wire required to cover the curved surface of the cylinder completely is approximately 1256 cm.
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A wire of diameter 3mm is wound about a cylinder whose height is 12cm and radius 5cm so as to cover the curved surface completely. Then the length of the wire is?
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A wire of diameter 3mm is wound about a cylinder whose height is 12cm and radius 5cm so as to cover the curved surface completely. Then the length of the wire is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A wire of diameter 3mm is wound about a cylinder whose height is 12cm and radius 5cm so as to cover the curved surface completely. Then the length of the wire is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire of diameter 3mm is wound about a cylinder whose height is 12cm and radius 5cm so as to cover the curved surface completely. Then the length of the wire is?.
A wire of diameter 3mm is wound about a cylinder whose height is 12cm and radius 5cm so as to cover the curved surface completely. Then the length of the wire is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A wire of diameter 3mm is wound about a cylinder whose height is 12cm and radius 5cm so as to cover the curved surface completely. Then the length of the wire is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire of diameter 3mm is wound about a cylinder whose height is 12cm and radius 5cm so as to cover the curved surface completely. Then the length of the wire is?.
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