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) ?
3π/2
π/2
2π
π
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CISF-AC-EXE – 2021
The inscribed circle is tangent to all four sides of the square. Its diameter is equal to the side length of the square.
Radius of the inscribed circle (r_in) = s/2 = 2/2 = 1 m.
Area of the inscribed circle = π * (r_in)² = π * (1)² = π m².
The circumscribed circle passes through all four vertices of the square. Its diameter is equal to the length of the diagonal of the square.
Diagonal of the square = s * √2 = 2 * √2 m.
Radius of the circumscribed circle (r_circum) = (diagonal)/2 = (2√2)/2 = √2 m.
Area of the circumscribed circle = π * (r_circum)² = π * (√2)² = π * 2 = 2π m².
The difference of the areas = Area of circumscribed circle – Area of inscribed circle
Difference = 2π m² – π m² = π m².