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A rope makes 70 rounds of the circumference of a cylinder whose radius of the base is14 cm How many times can it go round a cylinder with radius 20 cm?
- a)40
- b)49
- c)100
- d)54
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A rope makes 70 rounds of the circumference of a cylinder whose radius...
To solve this problem, we need to understand the relationship between the radius of the cylinder and the length of the rope.
1. Understanding the relationship:
The circumference of a circle is given by the formula: C = 2πr, where C is the circumference and r is the radius.
Since the rope makes 70 rounds of the circumference of the cylinder with a radius of 14 cm, the length of the rope is equal to 70 times the circumference of the cylinder with a radius of 14 cm.
2. Finding the length of the rope:
The circumference of a cylinder with a radius of 14 cm is given by: C1 = 2π(14) = 28π cm.
So, the length of the rope is: L1 = 70 * C1 = 70 * 28π cm.
3. Finding the number of times the rope can go around the cylinder with a radius of 20 cm:
Now, we need to find how many times the rope can go around a cylinder with a radius of 20 cm.
The circumference of a cylinder with a radius of 20 cm is given by: C2 = 2π(20) = 40π cm.
Let's assume the rope can go around this cylinder "n" times.
So, the length of the rope will be: L2 = n * C2 = n * 40π cm.
4. Equating the lengths of the rope:
Since the length of the rope remains the same, we can equate L1 and L2:
70 * 28π = n * 40π
Simplifying, we get:
n = (70 * 28π) / (40π)
n = (7/4) * 70
n = 49
Therefore, the rope can go around the cylinder with a radius of 20 cm 49 times.
Hence, the correct answer is option B) 49.
1. Understanding the relationship:
The circumference of a circle is given by the formula: C = 2πr, where C is the circumference and r is the radius.
Since the rope makes 70 rounds of the circumference of the cylinder with a radius of 14 cm, the length of the rope is equal to 70 times the circumference of the cylinder with a radius of 14 cm.
2. Finding the length of the rope:
The circumference of a cylinder with a radius of 14 cm is given by: C1 = 2π(14) = 28π cm.
So, the length of the rope is: L1 = 70 * C1 = 70 * 28π cm.
3. Finding the number of times the rope can go around the cylinder with a radius of 20 cm:
Now, we need to find how many times the rope can go around a cylinder with a radius of 20 cm.
The circumference of a cylinder with a radius of 20 cm is given by: C2 = 2π(20) = 40π cm.
Let's assume the rope can go around this cylinder "n" times.
So, the length of the rope will be: L2 = n * C2 = n * 40π cm.
4. Equating the lengths of the rope:
Since the length of the rope remains the same, we can equate L1 and L2:
70 * 28π = n * 40π
Simplifying, we get:
n = (70 * 28π) / (40π)
n = (7/4) * 70
n = 49
Therefore, the rope can go around the cylinder with a radius of 20 cm 49 times.
Hence, the correct answer is option B) 49.
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A rope makes 70 rounds of the circumference of a cylinder whose radius of the base is14cmHow many times can it go round a cylinder with radius20cm?a)40b)49c)100d)54Correct answer is option 'B'. Can you explain this answer? for Class 8 2025 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A rope makes 70 rounds of the circumference of a cylinder whose radius of the base is14cmHow many times can it go round a cylinder with radius20cm?a)40b)49c)100d)54Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 8 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rope makes 70 rounds of the circumference of a cylinder whose radius of the base is14cmHow many times can it go round a cylinder with radius20cm?a)40b)49c)100d)54Correct answer is option 'B'. Can you explain this answer?.
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