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Appropriate Question :-

The figure below shows a rope that circles the Earth. The radius of the Earth is 6371 kilometers. Assuming the rope makes a perfect circle, what is the length of this rope? Give your answer in terms of pi. kilometers.

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Solution :-

Given Information :-

  • Radius of Earth ➢ 6,371 km
  • A rope completely circles the Earth
  • Earth is a circle

To Find :-

  • The Length of rope in terms of π ( pi. )

Formula Used :-

  • [tex]\pmb{ \bold{ \underline{ \boxed{\boxed{ \sf {perimeter \: of \: circle \:(circumference)= \red{ 2\pi r}}}}}}}[/tex]

Calculation :-

∵ The rope completely circles the Earth

⇒ Length of the rope = Perimeter of the Earth

∵ Formula to calculate the perimeter (circumference) = 2πr

∵ Earth is mentioned as a circle here, it's radius is 6,371 km

Substituting the values in the formula, We get,

⇒ Perimeter of Earth = 2 × π × 6,371 km

Calculating further, We get,

⇒ Perimeter of Earth = 12,742π km

As stated earlier, perimeter of Earth = length of rope

⇒ The perimeter of Earth is 12,742π km

∴ The length of the rope is 12,742π km

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Final Answer :-

The Length of rope circling the Earth in terms of π ( pi. ) is 12,742 km.

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Note :-

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