Multiple choice

In a circle of radius $7$ cm, arc $AB$ makes one angle $\displaystyle 90^{\circ}$ at the centre O. Find the length of the major arc $AB$.

  1. $28$ cm
  2. $31$ cm
  3. $33$ cm
  4. $35$ cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The circumference of the circle is 2 * pi * r = 2 * pi * 7 = 14 * pi. The minor arc for a 90 degree angle is 1/4 of the circumference, which is 3.5 * pi. The major arc is the remaining 3/4 of the circumference, which is 10.5 * pi, approximately 33 cm.

AI explanation

The total angle around the center O is 360 degrees, so the major arc AB corresponds to an angle of 360 - 90 = 270 degrees. The length of an arc is given by the formula (angle/360) * 2 * pi * r, where r is the radius of 7 cm. Substituting the values gives (270/360) * 2 * (22/7) * 7 = 0.75 * 44 = 33 cm. The length of the major arc AB is 33 cm.

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