ashlynnrogue1
Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

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.

Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.