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14. A copper wire of diameter 8 mm is evenly wrapped on a cylinder of length 24 cm and
diameter 49 cm to cover the whole surface. Find (i) the length of the wire (ii) the volume of
the wire.?
diameter 49 cm to cover the whole surface. Find (i) the length of the wire (ii) the volume of
the wire.?
Most Upvoted Answer
14. A copper wire of diameter 8 mm is evenly wrapped on a cylinder of ...
Length of the Wire
To determine the length of the copper wire wrapped around the cylinder, we first calculate the circumference of the cylinder:
- Diameter of the cylinder = 49 cm
- Radius of the cylinder = 49/2 = 24.5 cm
- Circumference (C) = 2 * π * Radius = 2 * π * 24.5 cm ≈ 154.5 cm
Next, we calculate the number of turns made by the wire:
- Diameter of the wire = 8 mm = 0.8 cm
- The vertical distance covered in one complete turn = Diameter of the wire = 0.8 cm
Now, calculate the number of turns:
- Total height of the cylinder = 24 cm
- Number of turns = Total height / Diameter of wire = 24 cm / 0.8 cm = 30 turns
Finally, the total length of the wire (L) is:
- Length of the wire = Circumference * Number of turns = 154.5 cm * 30 ≈ 4635 cm
Volume of the Wire
To find the volume of the wire, we can use the formula for the volume of a cylinder:
- Volume (V) = π * r^2 * h
Where:
- r = radius of the wire = Diameter/2 = 0.8 cm/2 = 0.4 cm
- h = length of the wire = 4635 cm
Now, substituting the values:
- Volume = π * (0.4 cm)^2 * 4635 cm
- Volume ≈ 3.14 * 0.16 cm^2 * 4635 cm ≈ 2263.8 cm^3
Summary
- Length of the wire: 4635 cm
- Volume of the wire: 2263.8 cm^3
To determine the length of the copper wire wrapped around the cylinder, we first calculate the circumference of the cylinder:
- Diameter of the cylinder = 49 cm
- Radius of the cylinder = 49/2 = 24.5 cm
- Circumference (C) = 2 * π * Radius = 2 * π * 24.5 cm ≈ 154.5 cm
Next, we calculate the number of turns made by the wire:
- Diameter of the wire = 8 mm = 0.8 cm
- The vertical distance covered in one complete turn = Diameter of the wire = 0.8 cm
Now, calculate the number of turns:
- Total height of the cylinder = 24 cm
- Number of turns = Total height / Diameter of wire = 24 cm / 0.8 cm = 30 turns
Finally, the total length of the wire (L) is:
- Length of the wire = Circumference * Number of turns = 154.5 cm * 30 ≈ 4635 cm
Volume of the Wire
To find the volume of the wire, we can use the formula for the volume of a cylinder:
- Volume (V) = π * r^2 * h
Where:
- r = radius of the wire = Diameter/2 = 0.8 cm/2 = 0.4 cm
- h = length of the wire = 4635 cm
Now, substituting the values:
- Volume = π * (0.4 cm)^2 * 4635 cm
- Volume ≈ 3.14 * 0.16 cm^2 * 4635 cm ≈ 2263.8 cm^3
Summary
- Length of the wire: 4635 cm
- Volume of the wire: 2263.8 cm^3
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14. A copper wire of diameter 8 mm is evenly wrapped on a cylinder of length 24 cm and diameter 49 cm to cover the whole surface. Find (i) the length of the wire (ii) the volume of the wire.?
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14. A copper wire of diameter 8 mm is evenly wrapped on a cylinder of length 24 cm and diameter 49 cm to cover the whole surface. Find (i) the length of the wire (ii) the volume of the wire.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 14. A copper wire of diameter 8 mm is evenly wrapped on a cylinder of length 24 cm and diameter 49 cm to cover the whole surface. Find (i) the length of the wire (ii) the volume of the wire.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 14. A copper wire of diameter 8 mm is evenly wrapped on a cylinder of length 24 cm and diameter 49 cm to cover the whole surface. Find (i) the length of the wire (ii) the volume of the wire.?.
14. A copper wire of diameter 8 mm is evenly wrapped on a cylinder of length 24 cm and diameter 49 cm to cover the whole surface. Find (i) the length of the wire (ii) the volume of the wire.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 14. A copper wire of diameter 8 mm is evenly wrapped on a cylinder of length 24 cm and diameter 49 cm to cover the whole surface. Find (i) the length of the wire (ii) the volume of the wire.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 14. A copper wire of diameter 8 mm is evenly wrapped on a cylinder of length 24 cm and diameter 49 cm to cover the whole surface. Find (i) the length of the wire (ii) the volume of the wire.?.
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