A piece of wire in the form of the rectangle of the length $7 c m$ and breadth $4 c m$ is refolded in the form of the circle. Find the radius of the circle.

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3.5cm

4.5cm

5.5cm

5.3cm

answer is A.

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Detailed Solution

Here it is shown that a piece of wire in the shape of a rectangle with a length of 7 cm and a width is 4 cm folded into a circle shape, so now we can say that both will have the same length of the total border as the wire is the same, which is again folded into different shapes.
Let be the radius of the wire R and the total length of the wire l and convert the same wire from a rectangle to a circle which is

Here

is a rectangle formed by a piece of wire that is converted to a circle with center O and radius

and as now we assumed that the total length of the wire is L and the total length would be equal to the perimeter of the rectangle.
So,

total length of the wire=perimeter of the rectangle ABCD

And we know that the perimeter of the rectangle is given by

2 (l + b)

and in this question

l = 7 c m, b = 4 c m

So total length of piece of wire

L = 2 (l + b)

L = 2 7 + 4 c m L = 211 = 22 c m

If we change the shape, then the total length of the wire will remain the same and will be equal to the circumference of the circle, which is given by

.
So we can say that