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 :
40 cm
42 cm
41 cm
35 cm
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CISF-AC-EXE – 2023
– Rectangle sides are in the ratio 6:7. Let the sides be 6x and 7x.
– Area of rectangle = length * width = (6x)(7x) = 42x².
– Given area = 4200 sq. cm.
– 42x² = 4200 => x² = 4200 / 42 = 100 => x = 10 cm.
– Sides of the rectangle are 6 * 10 = 60 cm and 7 * 10 = 70 cm.
– Perimeter of rectangle = 2 * (length + width) = 2 * (60 + 70) = 2 * 130 = 260 cm.
– Circumference of the circle = 2πr, where r is the radius.
– Perimeter of circle = Perimeter of rectangle => 2πr = 260 cm.
– πr = 130 cm.
– r = 130 / π.
– Using the approximation π ≈ 3.14: r ≈ 130 / 3.14 ≈ 41.40 cm.
– Using the approximation π ≈ 22/7: r ≈ 130 / (22/7) = 130 * 7 / 22 = 910 / 22 = 455 / 11 ≈ 41.36 cm.
– The value approximately matches 41 cm.