Multiple choice

A chord AB of a circle of radius $10$cm makes a right angle at the centre of the circle. Find the area of the major and minor segments (Take $\pi=3.14$)

  1. Area of major segment$=285.5cm^2$,  Area of minor segment$=28.5cm^2$
  2. Area of major segment$=232cm^2$,  Area of minor segment$=24.6cm^2$
  3. Area of major segment$=212.7cm^2$,  Area of minor segment$=32.5cm^2$
  4. Area of major segment$=196.2cm^2$,  Area of minor segment$=21.3cm^2$
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A Correct answer
Explanation

For a circle with radius 10 and a 90-degree central angle, the area of the minor segment is (pi*r^2 * 90/360) - (0.5 * r^2 * sin(90)) = (3.14 * 100 / 4) - 50 = 78.5 - 50 = 28.5 cm^2. The major segment area is total area - minor segment = 314 - 28.5 = 285.5 cm^2.

AI explanation

The area of the quadrant is (90/360) times 3.14 times 100, equaling 78.5 square cm. The area of the right triangle is half times 10 times 10, which is 50 square cm. The area of the minor segment is 78.5 minus 50, resulting in 28.5 square cm. The area of the major segment is the total area of the circle minus the minor segment, so 314 minus 28.5 equals 285.5 square cm.

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