Multiple choice

A copper wire when bent in the form of a square encloses an area of 484 sq cm if the same wire is bent in the form of a circle the area enclosed by it is (Use $\displaystyle \pi =\frac{22}{7} $)

  1. 412 $\displaystyle cm^{2} $
  2. 616 $\displaystyle cm^{2} $
  3. 500 $\displaystyle cm^{2} $

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A square with area 484 has a side of 22 cm, so the perimeter (wire length) is 88 cm. A circle with circumference 88 cm has a radius r = 88 / (2 * 22/7) = 14 cm. The area of the circle is pi * r^2 = (22/7) * 14 * 14 = 616 sq cm.

AI explanation

First, find the side of the square using the area formula, which gives a side of sqrt(484) = 22 cm. The perimeter of the square, and thus the length of the wire, is 4 * 22 = 88 cm. When bent into a circle, this becomes the circumference, so 2 * (22/7) * r = 88, yielding a radius of 14 cm. The area of the circle is (22/7) * 14^2 = 616 sq cm.

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