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The area of a circle is 9π in². What is the circumference, in inches? Express your answer in terms of \piπ

Sagot :

Answer:

[tex]6\pi[/tex] in

Step-by-step explanation:

The formula to find the area of a circle: [tex]\pi r^{2}[/tex], where [tex]r[/tex] is the radius.

The formula to find the circumference (perimeter) of a circle: [tex]2\pi r[/tex], where [tex]r[/tex] is the radius.

1) To find the circumference of the circle, we need to find the radius ([tex]r[/tex]) first. Since the area of the circle is given to us, we need to equate this to the formula to find the area of a circle.

[tex]9\pi =\pi r^2[/tex]

Cancel the [tex]\pi[/tex] by bringing it to the other side.

[tex]9 =\pi r^2[/tex] ÷ [tex]\pi[/tex]

[tex]9 = r^2\\\sqrt{9} = r\\3 = r[/tex]

2) Find the circumference of the circle by using the formula, [tex]2\pi r[/tex].

=  [tex]2*\pi *3[/tex]

= [tex]6\pi[/tex] in