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Advocard [28]
3 years ago
15

A sector with radius of 8cm has an area of 56cm^2 what is the central angle of the sector in radians

Mathematics
1 answer:
xeze [42]3 years ago
7 0

Answer:

\frac{49\pi}{88}\,\,radians

Step-by-step explanation:

Given: Radius of sector is 8 cm

Area of sector is 56\,\,cm^2

To find: central angle of the sector

Solution:

Area of sector = \frac{\theta }{360^{\circ}}\pi r^2

Here, r is the radius of the sector and \theta is the central angle of the sector

56=\frac{\theta }{360^{\circ}}\left ( \frac{22}{7} \right ) (8)^2\\\theta =\frac{56\times 360\times 7}{22\times 64}=\left ( \frac{2205}{22} \right )^{\circ}

Using 1 degree = \frac{\pi}{180} radians

So,

\theta =\left ( \frac{2205}{22} \right )^{\circ}\\=\left ( \frac{2205}{22} \right )^{\circ}\times \frac{\pi}{180}\\=\frac{49\pi}{88}\,\,radians

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