Multiple choice

Find the ratio of areas of inscribed square in a semi-circle and a circle while the radii of circle and semi-circle are equal :

  1. 2 : 5

  2. 3 : 5

  3. 4 : 5

  4. 1 : 5
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A Correct answer
AI explanation

For a square inscribed in a full circle of radius r, the diagonal is the diameter, giving an area of 2r squared. For a square inscribed in a semicircle, if the side is a, the radius r squared equals a squared plus (a/2) squared, making the area 4r squared divided by 5. The ratio of the semicircle square area to the full circle square area is (4/5)r squared to 2r squared, which simplifies to 2 to 5.

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