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? (Take π = 3.14)

To solve this problem, we will calculate the length of the cord required for both the circular pipe and the square box, then compare them to see if any cord is left.

Step 1: Length of cord required for the circular pipe
The cord is wrapped around the circumference of the circular pipe. The formula for the circumference of a circle is:

Circumference = 2 * π * radius

Given:

Radius of the circular pipe = 4 cm
π = 3.14
So, the circumference of the circular pipe is:

Circumference = 2 * 3.14 * 4 = 25.12 cm

Step 2: Length of cord required for the square box
The cord is wrapped around the perimeter of the square box. The formula for the perimeter of a square is:

Perimeter = 4 * side

Given:

Side of the square box = 4 cm
So, the perimeter of the square box is:

Perimeter = 4 * 4 = 16 cm

Step 3: Compare the lengths
Length of cord required for the circular pipe = 25.12 cm
Length of cord required for the square box = 16 cm
Now, we check if there is any cord left. Pragya initially wrapped the cord around the circular pipe, and after cutting it, she used it to wrap the square box. The total length of cord used is:

Total length used = Length for circular pipe + Length for square box Total length used = 25.12 cm + 16 cm = 41.12 cm

Since the cord is cut to the required length, if Pragya started with a cord of exactly 41.12 cm, there would be no cord left.

Conclusion:
Pragya used up the entire cord, so she did not have any cord left.