In a pie-diagram (with radius 7 cm), the central angles of the sectors are in the ratio 2 : 3 : 7 : 5 : 1. (Take π = 22/7) If p is the perimeter of the smallest sector, then what is the value of 9p?
A.142 cm
B.148 cm✓ Correct
C.156 cm
D.221 cm
Explanation
Smallest sector angle = (1/18) × 360° = 20°. Arc length = (20/360) × 2π × 7 = (1/18) × 44 = 44/18 = 22/9 cm. Perimeter of sector = arc + 2 radii = 22/9 + 14 = (22 + 126)/9 = 148/9 cm. So 9p = 148 cm.
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