Multiple choice

In a circle of radius 21 cm, an arc subtends an angle of 72° at the centre. The length of the arc is

  1. 21.6 cm

  2. 26.4 cm

  3. 13.2 cm

  4. 19.8 cm

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Arc length = (theta/360) * 2 * pi * r = (72/360) * 2 * (22/7) * 21 = (1/5) * 2 * 22 * 3 = 132/5 = 26.4 cm.

AI explanation

The formula for the length of an arc is L equals 2 times pi times r times the central angle, divided by 360. Substituting the given radius of 21 cm and the angle of 72 degrees gives L equals 2 times pi times 21 times 72, all divided by 360. This simplifies to 42 times pi times one-fifth, which equals 8.4 times pi. Using the standard approximation of 22/7 for pi yields 26.4 cm.