Pragya wound a string around a pipe with a radius of 4 cm (see accompanying diagram) and cut it to the length needed. She then wrapped it around a 4-cm-square box (also shown). How much cord still remains?

# Pragya wound a string around a pipe with a radius of 4 cm (see accompanying diagram) and cut it to the length needed. She then wrapped it around a 4-cm-square box (also shown). How much cord still remains?

1. A
9.12 cm
2. B
12.9 cm
3. C
9.24 cm
4. D
1.92 cm

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### Solution:

Concept: Any object that is wrapped with cord has a length equal to its circumference. To determine if there is any cord left, we will measure the length of cord that has been wrapped around the circle and square.
Now, a circle's perimeter is equal to , or r, in units. As Pragya encircled a pipe with a 4 cm radius with a cord.
Therefore, Length of cord wrapped equals Circumference of circle So, the circumference of the circle's cord is 25.12 cm long.
Pragya has now encircled a square with a 4 cm side with the cord. Now, the square's perimeter equals 4a, where an is one of its sides.
Therefore, string length wrapped equals square perimeter As a result, 16 cm of the cord's length is wrapped around the square.
Now, we can observe that the cord's circumference in a square is equal to its circumference in a circle. So, there is still some cord left. Therefore, we shall subtract the two lengths to determine the remaining cable.
Cord remaining = circle wrapped cord length minus square wrapped cord length
Cord left: Therefore, there is 9.12 cm of cord left.
Hence, option 1 is correct.

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