Multiple choice

If the diagonal of a square is 10√2 cm then find the maximum circumference of a circle that can be inscribed in the square?

  1. 61.50 cm

  2. 31.43 cm

  3. 86.25 cm

  4. Cannot be determined

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

Diagonal of square = side * sqrt(2) = 10*sqrt(2). So side = 10. The diameter of the inscribed circle is equal to the side of the square, so diameter = 10. Circumference = pi * diameter = 3.14159 * 10 = 31.4159, which is approximately 31.43.

AI explanation

The side length of a square is its diagonal divided by the square root of 2, which gives 10 times the square root of 2 divided by the square root of 2, equaling 10 cm. A circle inscribed in this square has a diameter equal to the side of the square, so its radius is 5 cm. The circumference of this inscribed circle is 2 times pi times the radius, which equals 10 pi cm. Using the approximation of pi as 3.1416, the circumference is 31.42 cm, which rounds to 31.43 cm.

Keep practicing — related questions