ashlynnrogue1
Answered

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What is the radius of a sector
when 0=2pi/3 radians and the
area is ?

100pi/
27
?
Enter

What Is The Radius Of A Sector When 02pi3 Radians And The Area Is 100pi 27 Enter class=

Sagot :

Answer:

[tex]\frac{10}{3}[/tex] units

Step-by-step explanation:

Recall that the area of a sector is [tex]A=\frac{r^2\theta}{2}[/tex] where [tex]r[/tex] is the radius and [tex]\theta[/tex] is the angle of the sector (measured in radians).

Therefore, the radius of the sector is:

[tex]A=\frac{r^2\theta}{2}[/tex]

[tex]\frac{100\pi}{27}=\frac{r^2(\frac{2\pi}{3})}{2}[/tex]

[tex]200\pi=27r^2(\frac{2\pi}{3})[/tex]

[tex]200\pi=r^2(\frac{54\pi}{3})[/tex]

[tex]200\pi=r^2(18\pi)[/tex]

[tex]\frac{200}{18}=r^2[/tex]

[tex]\frac{100}{9}=r^2[/tex]

[tex]\frac{10}{3}=r[/tex]

So, the radius of the sector is [tex]\frac{10}{3}[/tex] units.

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