The perimeter of a sector of a circle of radius 4cm is (\(\pi + 8\))cm. Calculate the anle of the sector
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Correct Answer: Option A
Explanation:
Perimeter of sector = 2r + \(\frac{\theta}{360^o} \times 2\pi r\)
\(\pi + 8 = 2 \times 4 + \frac{\theta}{3360^o} \times 2 \pi \times 4\)
\(\pi + 8 + \frac{\theta}{360^o} \times 8 \pi\)
P + 8 - 8 = \(\frac{\theta \pi}{456o}\)
\(\pi = \frac{\theta \pi}{45^o}\)
\(\theta \pi = 45^o\)
Perimeter of sector = 2r + \(\frac{\theta}{360^o} \times 2\pi r\)
\(\pi + 8 = 2 \times 4 + \frac{\theta}{3360^o} \times 2 \pi \times 4\)
\(\pi + 8 + \frac{\theta}{360^o} \times 8 \pi\)
P + 8 - 8 = \(\frac{\theta \pi}{456o}\)
\(\pi = \frac{\theta \pi}{45^o}\)
\(\theta \pi = 45^o\)