Maximum area of the rectangle inscribed in a circle of radius 10 cms is
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100
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200
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300
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400
For a rectangle inscribed in a circle of radius R, the area is maximized when the rectangle is a square. The diagonal of the square is the diameter of the circle, which is 2R = 20. If the side of the square is s, s^2 + s^2 = 20^2 = 400. 2s^2 = 400, s^2 = 200. The area of the square is s^2 = 200.
The maximum area of a rectangle inscribed in a circle occurs when the rectangle is a square. The diagonal of this square equals the diameter of the circle, which is 2 multiplied by 10 or 20 cm. The side length of the square is found by dividing the diagonal by the square root of 2, yielding 10 times the square root of 2. The area is the side length squared, which is (10 times the square root of 2) squared, resulting in an area of 200 square centimeters. The correct answer is 200.