Multiple choice

A chord of a circle of radius $6\ cm$ subtends a right angle at centre. The area of the minor segment $(\pi=3.14)$ is____.

  1. $9.82\ cm^{2}$
  2. $10.14\ cm^{2}$
  3. $10.26\ cm^{2}$
  4. $12.35\ cm^{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Area of sector = (90/360) * pi * r^2 = 0.25 * 3.14 * 36 = 28.26. Area of triangle = 0.5 * r^2 = 0.5 * 36 = 18. Area of segment = 28.26 - 18 = 10.26.

AI explanation

The area of the minor segment is the area of the sector minus the area of the right-angled triangle. The sector area is $(90/360) \times \pi \times 6^2 = 28.26$ cm$^2$. The area of the triangle is $(1/2) \times 6 \times 6 = 18$ cm$^2$. Subtracting the triangle from the sector gives $28.26 - 18 = 10.26$ cm$^2$.

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