The central angle measure of the sector is 4.19 rad.
Area of a Sector
You need apply the formula: [tex]A= r^2*\frac{\alpha}{2}[/tex] for finding the area of the sector, in radians. In this formula, the variables are:
r= radius
[tex]\alpha[/tex]= central angle
The question gives:
A=54[tex]\pi[/tex] cm²
r= radius= 9cm
Thus, the central angle will be:
[tex]A= r^2*\frac{\alpha}{2}\\ \\ 54\pi =81*\frac{\alpha }{2} \\ \\ 1.33333\pi =\alpha[/tex]
For [tex]\pi[/tex]=3.14159..., you have :
[tex]\alpha=4.19\; rad[/tex]
Read more about the area of a sector here:
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