Question

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

Answer 1

Given: An sector with a central angle-

$\theta=\frac{2\pi}{3}$

And area,

$Area=\frac{100\pi}{27}\text{ sq units}$

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-

$Area=\frac{1}{2}r^2\theta\text{ sq units}$

Substituting the values into the formula as-

$\frac{100\pi}{27}=\frac{1}{2}(\frac{2\pi}{3})r^2$

Further solving for 'r' as follows-

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

Final Answer: The radius of the sector is-

$r=\frac{10}{3}\text{ units}$