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A rope makes 140 rounds of the circumference of a cylinder, the radius of whose base is 14cm. How many times can it go round a cylinder with radius 20cm?
- a)98
- b)49
- c)490
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A rope makes 140 rounds of the circumference of a cylinder, the radius...
Length of rope = 2πr × 140
Number of rounds =
Number of rounds =
Most Upvoted Answer
A rope makes 140 rounds of the circumference of a cylinder, the radius...
To solve this problem, we can use the formula for the circumference of a cylinder, which is given by:
C = 2πr
where C is the circumference and r is the radius of the base.
Given that the radius of the first cylinder is 14 cm, we can calculate its circumference as follows:
C1 = 2π(14) = 28π cm
Since the rope makes 140 rounds of the circumference of the first cylinder, the length of the rope is 140 times the circumference of the first cylinder:
L1 = 140 * C1 = 140 * 28π cm
Now, let's calculate the circumference of the second cylinder, which has a radius of 20 cm:
C2 = 2π(20) = 40π cm
We want to find out how many times the rope can go round the second cylinder, so we need to calculate the length of the rope that corresponds to one complete round of the second cylinder. This length is equal to the circumference of the second cylinder:
L2 = C2 = 40π cm
To find out how many times the rope can go round the second cylinder, we can divide the length of the rope (L1) by the length of one round of the second cylinder (L2):
Number of rounds = L1 / L2 = (140 * 28π) / (40π) = (140 * 28) / 40 = 98
Therefore, the rope can go round the cylinder with a radius of 20 cm 98 times. So the correct answer is option B.
C = 2πr
where C is the circumference and r is the radius of the base.
Given that the radius of the first cylinder is 14 cm, we can calculate its circumference as follows:
C1 = 2π(14) = 28π cm
Since the rope makes 140 rounds of the circumference of the first cylinder, the length of the rope is 140 times the circumference of the first cylinder:
L1 = 140 * C1 = 140 * 28π cm
Now, let's calculate the circumference of the second cylinder, which has a radius of 20 cm:
C2 = 2π(20) = 40π cm
We want to find out how many times the rope can go round the second cylinder, so we need to calculate the length of the rope that corresponds to one complete round of the second cylinder. This length is equal to the circumference of the second cylinder:
L2 = C2 = 40π cm
To find out how many times the rope can go round the second cylinder, we can divide the length of the rope (L1) by the length of one round of the second cylinder (L2):
Number of rounds = L1 / L2 = (140 * 28π) / (40π) = (140 * 28) / 40 = 98
Therefore, the rope can go round the cylinder with a radius of 20 cm 98 times. So the correct answer is option B.
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A rope makes 140 rounds of the circumference of a cylinder, the radius of whose base is 14cm. How many times can it go round a cylinder with radius 20cm?a)98b)49c)490d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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