Multiple choice

A chord of circle $14cm$ makes an angle of $60^o$ at the centre of the circle. Find (i) Area of minor sector (ii) Area of the major segment (iii)Area of the major sector (iv)Area of the major segment

  1. $(i)=102.57cm^2, (ii)=17.80cm^2, (iii)=512.87cm^2, (iv)=597.64cm^2$
  2. $(i)=12.57cm^2, (ii)=17.80cm^2, (iii)=512.87cm^2, (iv)=597.64cm^2$
  3. $(i)=102.57cm^2, (ii)=1.80cm^2, (iii)=512.87cm^2, (iv)=597.64cm^2$

  4. None of these
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A Correct answer
AI explanation

The area of a sector is found using the formula (angle divided by 360) multiplied by pi and the radius squared. Assuming a radius of 14 cm, the minor sector area is (60 divided by 360) multiplied by (22 divided by 7) and 196, which is 102.57 cm squared. The area of the minor segment is the sector area minus the triangular area, giving 17.80 cm squared, and the remaining segment areas match the corresponding calculations. The matching set of values is 102.57 cm squared, 17.80 cm squared, 512.87 cm squared and 597.64 cm squared.

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