A wire is in the shape of a circle. It is straightened and reshaped into a rectangle whose sides are in the ratio 6 : 7. If the area of the rectangle is 4200 sq. cm, the radius of circle is, approximately :

To find the radius of the circle, we first determine the dimensions of the rectangle. Let the sides of the rectangle be 6x and 7x.

Given the area of the rectangle is 4200 sq. cm:
6x × 7x = 4200
42x² = 4200
x² = 100 ⇒ x = 10 cm

The sides of the rectangle are 60 cm (6 × 10) and 70 cm (7 × 10). The perimeter of the rectangle is:
Perimeter = 2 × (Length + Breadth) = 2 × (60 + 70) = 260 cm

Since the same wire is reshaped from a circle to a rectangle, the circumference of the circle equals the perimeter of the rectangle:
2πr = 260
r = 260 / (2π) = 130 / π
Using π ≈ 3.14159:
r ≈ 130 / 3.14159 ≈ 41.38 cm

The closest approximate value among the options is 41 cm.