If p is the perimeter of the smallest sector, then what is the value of 9p?
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})
- A. 142 cm
- B. 148 cm ✓
- C. 156 cm
- D. 221 cm
Correct Answer: B. 148 cm
Explanation
The perimeter of a sector is the arc length plus two radii (2r). The arc length of the smallest sector (1 part out of 18) is \frac{1}{18} \times 2\pi r = \frac{1}{18} \times 2 \times \frac{22}{7} \times 7 = \frac{44}{18} = \frac{22}{9} cm. Adding the two straight radii, the full perimeter p = \frac{22}{9} + 14 = \frac{148}{9} cm. Multiplying this by 9 gives 9p = 148 cm.
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