Name: Perimeter of Semicircle: Illustration
Uploaded: 2019-07-19
Duration: 3 min 7 s
Description: You must have used a protractor to measure angles in your geometry classes. Do you know how to calculate the perimeter of it? Learn in this video.

Question

The radius of the Earth is approximately $6400 km$ . Suppose, a rope is wound around the equator once such that it is at a distance of $1 m$ from the surface at all points and, another rope is wound around the equator touching the surface of the Earth. Find the difference in the lengths of the two ropes.

If the same thing were to be done for a planet with a radius one sixty fourths the size of Earth, what would be the difference in the lengths of the ropes?

Accepted Answer

Given that, the radius of the Earth $= 6400 km$ (approx.)

We know that, the circumference of a circle of radius $r$ $= 2 π r$

A rope is wound around the equator once such that it is at a distance of $1 m$ from the surface at all points and another rope is wound around the equator touching the surface of the Earth.

Therefore, the radius of the smaller circle, $R_{1} = 6400 km = 6400000 m$ and the radius of the bigger circle, $R_{2} = (6400000 + 1) = 6400001 m$

So, the difference in the lengths of the two ropes

$= 2 π R_{2} - 2 π R_{1}$

$= 2 \times \frac{22}{7} \times (6400001 - 6400000) m$

$= \frac{44}{7} \times (1) m = \frac{44}{7} m$

Hence, the difference in the lengths of the ropes $= \frac{44}{7} m$ .

If the same thing were to be done for a planet with a radius one sixty fourths of the size of the Earth, then the radius of the planet $= \frac{6400}{64} km = 100 km$

Therefore, the radius of the smaller circle is $r_{1} = 100 km = 100000 m$ and the radius of the bigger circle is $r_{2} = (100000 + 1) = 100001 m$

So, the difference in the lengths of the two ropes

$= 2 π r_{2} - 2 π r_{1}$

$= 2 \times \frac{22}{7} \times (100001 - 100000) m$

$= \frac{44}{7} \times (1) = \frac{44}{7} m$

Therefore, the difference in the lengths of the ropes $= \frac{44}{7} m$ .

Important Questions on Perimeter and Area

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