What is the radius of a sectorradians and thesq units??when 0 = 23area is100TT27r =

Question

asked Sep 23, 2023 179k views

1 Answer

Miwoe · Answer 1 · 2023-09-28T05:42:18+0000

Given: An sector with a central angle-

$\theta=(2\pi)/(3)$

And area,

$Area=(100\pi)/(27)\text{ sq units}$

Required: To determine the radius of the sector.

Explanation: The area of the sector when the central angle is in radians is given by the formula-

$Area=(1)/(2)r^2\theta\text{ sq units}$

Substituting the values into the formula as-

$(100\pi)/(27)=(1)/(2)((2\pi)/(3))r^2$

Further solving for 'r' as follows-

$\begin{gathered} r=\sqrt{(100)/(9)} \\ r=(10)/(3)\text{ units} \end{gathered}$

Final Answer: The radius of the sector is-

$r=(10)/(3)\text{ units}$