Question

For the sector with central angle 45° and radius 16cm. Find the length of the arc and area.
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Answer 1

Length of the arc

=$\tt\huge{2\pi r}{\frac{\theta}{360}}$

=$\tt\huge{2\pi 16}{\frac{45}{360}}$

=$\tt\huge{2\pi 16}{\frac{\cancel {45} }{\cancel{360}\:\:\:8}}$

=$\huge{4\pi}$

=$\huge{12.57}$

Now, area of the sector:

=$\tt\huge{\pi r^2}{\frac{\theta}{360}}$

=$\tt\huge\frac{\pi r^2}{8}$

=$\tt\huge\frac{\pi 16^2}{8}$

=$\huge{32\pi}$

=$\huge{100.53cm^2}$

Answer 2

Solution :-

given that,

→ Central angle = 45°

→ Radius = 16 cm .

So,

→ Length of arc = (Central angle/360°) * 2 * π * radius

→ Length of arc = (45°/360°) * 2 * 3.14 * 16

→ Length of arc = (1/8) * 2 * 3.14 * 16

→ Length of arc = 4 * 3.14

→ Length of arc = 12.56 cm (Ans.)

also,

→ Area of sector = (Central angle/360°) * π * (radius)²

→ Area of sector = (45°/360°) * 3.14 * 16 * 16

→ Area of sector = (1/8) * 3.14 * 256

→ Area of sector = 32 * 3.14

→ Area of sector = 100.48 cm² (Ans.)

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