Multiple choice

The area of a square and a circle are same. If area of the square is $3696$ sq. cm, the distance covered when $8$ rounds are taken round the circle(approximately), is ________.

  1. $1724$cm
  2. $1700$cm
  3. $1800$cm
  4. $2000$cm
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A Correct answer
Explanation

Area of square = 3696. Side = sqrt(3696) approx 60.79. Area of circle = pi * r^2 = 3696. r = sqrt(3696/pi) approx 34.27. Circumference = 2 * pi * r = 2 * pi * 34.27 approx 215.3. Distance for 8 rounds = 8 * 215.3 = 1722.4. Closest option is 1724.

AI explanation

Since the areas are equal, the area of the circle is 3696, and using the formula for the area of a circle we set pi multiplied by the radius squared equal to 3696. Using 22 divided by 7 for pi gives a radius squared value of 1176, meaning the radius is approximately 34.29 centimeters. The circumference formula gives 2 multiplied by 22 divided by 7 and 34.29, yielding an approximate circumference of 215.5 centimeters. Taking 8 rounds around this circle gives 215.5 multiplied by 8, which equals approximately 1724 centimeters.