Multiple choice

The area of the circle is divided into three sectors in the respective ratio of 3 : 4 : 5 and the area of the circle is 45π. Quantity A 3π Quantity B Area of the second smallest sector

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be established from the information given.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total ratio parts = 3+4+5 = 12. Total area = 45pi. One part = 45pi / 12 = 3.75pi. Sectors are 3*3.75pi = 11.25pi, 4*3.75pi = 15pi, 5*3.75pi = 18.75pi. The second smallest sector is 15pi. Quantity B (15pi) is greater than Quantity A (3pi).

AI explanation

The circle's area is divided into three sectors in the ratio 3:4:5, which has a total of 12 parts. The second smallest sector corresponds to 4 out of the 12 parts, or one-third of the total area. Since the total area is 45 pi, the area of this sector is one-third of 45 pi, which equals 15 pi. Quantity B is 15 pi and Quantity A is 3 pi, so Quantity B is greater.

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