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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 45°, r = 16 cm
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Solution
central angle 45°, r = 16 cm
Length of the arc l = `theta^circ/(360^circ) xx 2pi"r" "units"`
l = `(45^circ)/(360^circ) xx 2 xx 3.14 xx 16 "cm"`
l = `1/8 xx 2 xx 3.14 xx 16 "cm"`
l = 12.56 cm
Area of the sector = `theta^circ/(360^circ) xx pi"r"^2 "sq. units"`
A = `(45^circ)/(360^circ) xx 3.14 xx 16 xx 16`
A = 100.48 cm2
Perimeter of the sector P = l + 2r units
P = 12.56 + 2(16) cm
P = 44.56 cm
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