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The area of a sector of a circle with a central angle of 170° is 70 m 2. find the radius of the circle. (round your answer to one decimal place.)

Respuesta :

Luv2Teach
The area of a sector of a circle is [tex]A= \frac{ \theta }{360} * \pi r^2[/tex].  We have everything but the radius to fill in there, so let's do it: [tex]70= \frac{170}{360} * \pi r^2[/tex].  To make it easy, cross out the last 0 in both the 170 and the 360, and then multiply both sides by 36 to get [tex]2520=17 \pi r^2[/tex].  Divide both sides by 17pi and you have 47.1847596=r^2 and r = 6.9
MrRoyal

The radius of the circle is 6.9 meters

How to determine the radius?

The sector area is given as:

A = 70 square meters

The central angle is:

Angle = 170 degrees

The area of the sector is calculated as:

[tex]A = \frac{\theta}{360} * \pi r^2[/tex]

So, we have:

[tex]70= \frac{170}{360} * 3.14 r^2[/tex]

Cross multiply

[tex]r^2 = \frac{360 * 70}{170 * 3.14}[/tex]

Evaluate

[tex]r^2 = 47.21[/tex]

Take the square root

r = 6.9

Hence, the radius of the circle is 6.9

Read more about sector area at:

https://brainly.com/question/16736105

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