Question

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

Answer 1

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,

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