Multiple choice

In a circle of radius $7$ cm, an arc subtends an angle of $\displaystyle 108^{\circ} $ at the centre. The area of the sector is $\displaystyle \left ( \pi =\frac{22}{7} \right )$

  1. $\displaystyle 43.2cm^{2}$
  2. $\displaystyle 44.2cm^{2}$
  3. $\displaystyle 45.2cm^{2}$
  4. $\displaystyle 46.2cm^{2}$
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D Correct answer
Explanation

Area = (theta/360) * pi * r^2 = (108/360) * (22/7) * 7^2 = 0.3 * 22 * 7 = 46.2.

AI explanation

The area of a sector of a circle is calculated using the formula (theta / 360) multiplied by pi multiplied by r squared. Substituting the given values, we get (108 / 360) multiplied by (22 / 7) multiplied by 7 squared. The fraction 108 / 360 simplifies to 3 / 10, which yields (3 / 10) multiplied by 22 multiplied by 7. Calculating this gives 46.2, so the area of the sector is 46.2 square centimeters.

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