Question

A sector with an area of \goldE{54\pi\,\text{cm}^2}54πcm

Answer 1

The central angle measure of the sector is 4.19 rad.

Area of a Sector

You need apply the formula: $A= r^2*\frac{\alpha}{2}$  for finding the area of the sector, in radians. In this formula, the variables are:

r= radius

$\alpha$= central angle

The question gives:

A=54$\pi$ cm²

r= radius= 9cm

Thus, the central angle will be:

$A= r^2*\frac{\alpha}{2}\\ \\ 54\pi =81*\frac{\alpha }{2} \\ \\ 1.33333\pi =\alpha$

For $\pi$=3.14159..., you have :

$\alpha=4.19\; rad$

Read more about the area of a sector here:

brainly.com/question/22972014

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