Question

a rope makes 140 rounds of the circumference of a cylinder the radius of whose base is 14 cm how many times can it go round of cylinder with radius 20 CM

Answer 1

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Answer 2

Given: A rope makes 140 rounds of the circumference of a cylinder the radius of whose base is 14 cm.

To find: Number of times the rope will go around the cylinder whose radius of base is 20 cm

Solution: Let the radius of the base of the first cylinder be r and radius of the base of the second cylinder be a.

Circumference of the base of the first cylinder

= 2 π r

= 2 × (22/7) × 14

= 88 cm

Since the rope makes 140 rounds of the cylinder, therefore the length of the rope is 140 times the circumference of the base of the cylinder.

Length of the rope

= 140 × Circumference of first cylinder

= 140 × 88

= 12320 cm

Now, Circumference of the base of the second cylinder

= 2πa

= 2 × (22/7) × 20

= 880/7 cm

Now, let the number of times it goes round the base of the second cylinder be n.

Therefore,

Length of the rope = n × Circumference of second cylinder

=> 12320 = n × (880/7)

=> n = 12320/ (880/7)

=> n = 98

Therefore, the rope can go 98 times around the cylinder with base area 20 cm.