Multiple choice

The angle of a sector in a given circle is $40$ degrees and the area of the sector is equal to $20 cm^2$ . Calculate the arc length of the sector.

  1. $6.5$ cm
  2. $7.4$ cm
  3. $5.3$ cm

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The area of a sector is given by A = (theta / 360) * pi * r^2, which means 20 = (40 / 360) * pi * r^2, so r = sqrt(180 / pi) approx 7.57 cm. The arc length is L = (theta / 360) * 2 * pi * r = (40 / 360) * 2 * pi * 7.57 approx 5.28 cm, which rounds to 5.3 cm.

AI explanation

Using the sector area formula A = (theta/360)*pi*r^2 with theta as 40 degrees and area as 20, we get 20 = (40/360)*pi*r^2, which simplifies to pi*r^2 = 180. The arc length formula is L = (theta/360)*2*pi*r, which can be rewritten as L = 2*A/r. Since r is the square root of (180/pi), the arc length calculates to approximately 5.3 cm.

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