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A sector with an area of \goldE{54\pi\,\text{cm}^2}54πcm
2
start color #a75a05, 54, pi, start text, c, m, end text, squared, end color #a75a05 has a radius of \maroonD{9\,\text{cm}}9cmstart color #ca337c, 9, start text, c, m, end text, end color #ca337c.
What is the central angle measure of the sector in radians?

A Sector With An Area Of GoldE54pitextcm254πcm 2 Start Color A75a05 54 Pi Start Text C M End Text Squared End Color A75a05 Has A Radius Of MaroonD9textcm9cmstar class=

Sagot :

Lhannearaujoidn

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:

brainly.com/question/22972014

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Answer:

4pi/3

Step-by-step explanation:

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