Question

Question: If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. θ= π/4 radians, A=84 squaremeters So r=?131.88m5.74m14.63m32.97m

Answer 1

Recall that the area of a sector of a circle of radius r formed by the central angle θ radians is:

$A=\frac{\theta}{2}r^2\text{.}$

Substituting θ=π/4, and A=84m² we get:

$84m^2=\frac{\frac{\pi}{4}}{2}r^2\text{.}$

Simplifying the above result we get:

$84m^2=\frac{\pi}{8}r^2.$

Multiplying the above equation by 8/π we get:

$\begin{gathered} 84m^2\times\frac{8}{\pi}=\frac{\pi}{8}r^2\times\frac{8}{\pi}, \\ r^2=\frac{672}{\pi}m^2\text{.} \end{gathered}$

Therefore:

$\begin{gathered} r=\sqrt[]{\frac{672}{\pi}}m \\ \approx14.63m \end{gathered}$

Answer: Third option, 14.63m.