Multiple choice

In a circle of radius 7 cm, an arc subtends an angle of 92° at the centre. Find the length of the arc and the area of the sector, respectively.

  1. 112.4 cm, 150.92 cm2

  2. 11.24 cm, 39.35 cm2

  3. 11.24 cm, 393.5 cm2

  4. 24.24 cm, 39.35 cm2
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B Correct answer
Explanation

Arc length = (theta/360) * 2 * pi * r = (92/360) * 2 * 3.14159 * 7 = 11.24 cm. Sector area = (theta/360) * pi * r^2 = (92/360) * 3.14159 * 49 = 39.35 cm^2.

AI explanation

Using the arc length formula of theta divided by 360 multiplied by 2 times pi times r, we get 92 divided by 360 times 2 times 22 divided by 7 times 7. This simplifies to 92 divided by 360 times 44, resulting in an arc length of 11.24 cm. For the sector area, applying the formula theta divided by 360 times pi times r squared gives 92 divided by 360 times 22 divided by 7 times 49, which equals 39.35 square cm.

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