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Question
For the sectors with given measures, find the length of the arc, area and perimeter. (π = 3.14)
central angle 120°, d = 12.6 cm
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Solution
∴ r = `12.6/2 "cm"`
r = 6.3 cm
Length of the arc l = `(theta^circ)/(360^circ) xx 2pi"r" "units"`
l = `(120^circ)/(360^circ) xx 2 xx 3.14 xx 63 "cm"`
l = 13.188 cm
I = 13.19 cm
Area of the sector A = `(theta^circ)/(360^circ) xx pi"r"^2 "units"`
A = `(120^circ)/(360^circ) xx 3.14 xx 6.3 xx 63 "cm"^2`
A = 3.14 × 6.3 × 2.1 cm2
A = 41.54 cm2
Perimeter of the sector P = l + 2r cm
P = 13.19 + 2(6.3) cm
= 13.19 + 12.6 cm
P = 25.79 cm
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