Question:
A cylinder 15 cms long has a circumference of 4 cms. A string makes exactly 5 turns around the cylinder, while its two ends touch the cylinder top and bottom. How long is the string?
A cylinder 15 cms long has a circumference of 4 cms. A string makes exactly 5 turns around the cylinder, while its two ends touch the cylinder top and bottom. How long is the string?
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For helical shapes, use the Pythagorean theorem to calculate the total length of the string or path.
Updated On: Jan 13, 2026
- 20 cms
- 22 cms
- 25 cms
- 28 cms
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the situation.
The string wraps around the cylinder 5 times. Since the circumference of the cylinder is 4 cm, the string makes 5 complete turns around the cylinder, so the length of the string is: \[ \text{Length of string} = 5 \times 4 = 20 \, \text{cms}. \] However, the string also spans vertically from the top to the bottom of the cylinder. The vertical distance is the height of the cylinder, which is 15 cm.
Step 2: Calculating the total length of the string.
The string forms a helical shape. We can calculate the length of the string using the Pythagorean theorem, where the horizontal distance is 20 cm and the vertical distance is 15 cm. Thus: \[ \text{Length of string} = \sqrt{20^2 + 15^2} = \sqrt{400 + 225} = \sqrt{625} = 25 \, \text{cms}. \]
Step 3: Conclusion.
Thus, the length of the string is (C) 25 cms.
The string wraps around the cylinder 5 times. Since the circumference of the cylinder is 4 cm, the string makes 5 complete turns around the cylinder, so the length of the string is: \[ \text{Length of string} = 5 \times 4 = 20 \, \text{cms}. \] However, the string also spans vertically from the top to the bottom of the cylinder. The vertical distance is the height of the cylinder, which is 15 cm.
Step 2: Calculating the total length of the string.
The string forms a helical shape. We can calculate the length of the string using the Pythagorean theorem, where the horizontal distance is 20 cm and the vertical distance is 15 cm. Thus: \[ \text{Length of string} = \sqrt{20^2 + 15^2} = \sqrt{400 + 225} = \sqrt{625} = 25 \, \text{cms}. \]
Step 3: Conclusion.
Thus, the length of the string is (C) 25 cms.
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