Multiple choice

The area $(in cm^2)$ of a sector of a circle with an angle of $45^o$ and radius $3$ cm is_.

  1. $3\dfrac{13}{14}$
  2. $4\dfrac{13}{14}$
  3. $3\dfrac{51}{56}$
  4. $3\dfrac{15}{28}$
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D Correct answer
Explanation

Area of sector = (theta/360) * pi * r^2 = (45/360) * (22/7) * 3^2 = 1/8 * 22/7 * 9 = 198 / 56 = 99 / 28 = 3 and 15/28.

AI explanation

The area of a sector is found using the formula Area = (theta / 360) * pi * r^2. Substituting the given values gives (45 / 360) * (22 / 7) * 3^2 = (1 / 8) * (22 / 7) * 9 = 198 / 56. Converting the improper fraction 198 / 56 to a mixed number gives 3 and 15/28. The result is 3 and 15/28.

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