If P is the area of the smallest sector and Q is the area of the largest sector, then what is P+Q equal to?

Consider the following for the next two (02) items that follow: In a pie-diagram (with radius 7 cm), the central angles of the sectors are in the ratio 2:3:7:5:1. (Take \pi=\frac{22}{7})

  1. A. \frac{88}{3} square cm
  2. B. \frac{77}{3} square cm
  3. C. \frac{149}{6} square cm
  4. D. \frac{616}{9} square cm

Correct Answer: D. \frac{616}{9} square cm

Explanation

The total of the ratio parts is 2+3+7+5+1 = 18 parts. The smallest sector (P) corresponds to 1 part, and the largest sector (Q) corresponds to 7 parts, making their sum 8 parts out of the 18 total parts. The total area of the pie diagram is \pi r^2 = \frac{22}{7} \times 7^2 = 154 sq cm. Therefore, the combined area P+Q = \frac{8}{18} \times 154 = \frac{4}{9} \times 154 = \frac{616}{9} square cm.

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