Question

Pragya wrapped a cord around a circular pipe of radius 4 cm (adjoining figure) and cut off the length required of the cost. Then she wrapped it around a square box of side 4 cm (also shown). Did she have any cord left? (Take $\pi {\text{ = 3}}{\text{.14}}$)

Answer 1

Hint: Cord wrapped around any object has a length equal to the perimeter of that object. We will find the length of cord wrapped around the circle and square and then subtract both of them to find if there is any cord left.

Complete step-by-step answer: -
Now, the perimeter of a circle = $2\pi {\text{r}}$ units, where r is the radius of the circle. As, Pragya wrapped a cord around a circular pipe of radius 4 cm.
 

So,
Length of cord wrapped = perimeter of circle = $2\pi {\text{r}}$ = 2 (3.14) (4)
So, length of cord wrapped around circle = 25.12 cm
Now, Pragya has wrapped the cord around a square of side 4 cm. Now, perimeter of square = 4a, where a is the side of square.

So, length of cord wrapped = perimeter of square = 4a = 4 x 4 = 16 cm.
So, the length of the cord is wrapped around a square = 16 cm.
Now, we can see that the length of cord wrapped around a circle is $ \ne $ length of cord wrapped around a square. So, a length of cord is still left. So, to find the cord left we will subtract the two lengths to get the answer.
Cord left = length of cord wrapped around circle – length of cord wrapped around square
Cord left = 25.12 – 16 = 9.12 cm
So, 9.12 cm length of cord is left.

Note: When we come up with such types of questions, to find the length of wire wrapped around an object, we have to find the perimeter of the object. To find the perimeter, we must know the shape of the object like rectangle, square, circle, etc. Correct formula should be applied to get the correct answer.