Multiple choice

For a circle of radius 21 m, find the difference between the areas of its sector of angle 120° and its corresponding major sector.

  1. 236 m2

  2. 462 m2

  3. 1386 m2

  4. 1400 m2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The area of a sector with angle theta is (theta/360) * pi * r^2. The difference between the major sector (360-120 = 240 degrees) and the minor sector (120 degrees) is (240-120)/360 * pi * r^2 = 1/3 * pi * 21^2 = 1/3 * 22/7 * 441 = 462.

AI explanation

The area of a sector is found by multiplying the circle area by the ratio of the sector angle to 360 degrees. The major sector constitutes the rest of the circle, so the difference between the major sector and the 120 degree minor sector is identical to the difference between the full circle area and twice the minor sector area. Calculating this gives pi times 21 squared minus 2 times 120 over 360 times pi times 21 squared, which results in 462 square meters.

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