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

`(49\pi)/(88)\,\,radians`

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 =
`(\theta )/(360^(\circ))\pi r^2`

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

`56=(\theta )/(360^(\circ))\left ( (22)/(7) \right ) (8)^2\\\theta =(56* 360* 7)/(22* 64)=\left ( (2205)/(22) \right )^(\circ)`

Using 1 degree =
`(\pi)/(180)` radians

So,

`\theta =\left ( (2205)/(22) \right )^(\circ)\\=\left ( (2205)/(22) \right )^(\circ)* (\pi)/(180)\\=(49\pi)/(88)\,\,radians`