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Q10 (CISF/2021) Science & Technology › Basic Science (Physics, Chemistry, Biology)

Consider a square of side length 2 m. What is the difference of the areas of the circumscribed circle and the inscribed circle (in m2) ?

Explanation

For a square with side length s = 2 m:

  1. Inscribed Circle: This circle touches the sides of the square, so its diameter is equal to the side of the square (d = 2 m). The radius r = s/2 = 1 m. The area is πr2 = π(1)2 = π m2.
  2. Circumscribed Circle: This circle passes through the vertices of the square, so its diameter is equal to the diagonal of the square. Using the Pythagorean theorem, diagonal = √(22 + 22) = √8 = 2√2 m. The radius R = (2√2)/2 = √2 m. The area is πR2 = π(√2)2 = 2π m2.
  3. Difference: The difference in areas = Area of circum
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