Multiple choice

The area of the sector of circle with radius 7 cm and of angle $\displaystyle 60^{\circ}$ is

  1. $\displaystyle \frac{144}{3}cm^{2}$
  2. $\displaystyle \frac{77}{3}cm^{2}$
  3. $\displaystyle \frac{154}{7}cm^{2}$

  4. None
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B Correct answer
Explanation

The area of a sector of a circle is calculated using the formula (theta / 360) * pi * r^2. Substituting the given values of theta = 60 degrees and r = 7 cm, we get (60 / 360) * (22 / 7) * 7^2. This simplifies to (1 / 6) * 154, which reduces to 77 / 3 square centimeters.

AI explanation

The area of a sector is found using the formula theta divided by 360, multiplied by pi times r squared. Substituting the given values, the area is 60 divided by 360, multiplied by 22/7 and 7 squared. This simplifies to 1/6 multiplied by 154, resulting in 77/3 square cm.

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