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Pragya wrapped a cord around a circular pipe of radius $4\ cm$ $(adjoining figure)$ and cut off the length required of the cord. Then she wrapped it around a square box of side $4\ cm$ $(also shown)$. Did she have any cord left? $(\pi=3.14)$
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Given: Pragya wrapped a cord around a circular pipe of radius $4\ cm$ $(adjoining figure)$ and cut off the length required of the cord. Then she wrapped it around a square box of side $4\ cm$ $(also shown)$

To do: To check whether she have any cord left? 

Solution:

Side of square box $=4\ cm$

The radius of circular pipe $=4\ cm$

Length of the cord $=$ Circumference of the circular pipe

$=2\pi r$

$=2\times 3.14\times 4\ cm$

$=25.12\ cm$

The perimeter of the square box $=4\times side$

$= 4\times 4\ cm$

$= 16\ cm$

Length of the cord left $=$ Circumference of the circular pipe-Perimeter of the square box

$= 25.12\ cm - 16\ cm$

$= 9.12\ cm$

Yes, $9.12\ cm$ cord is left.

Updated on: 10-Oct-2022

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