Respuesta :

skzmakemestay

Answer: 38.4845100065m²

when rounded to the nearest tenth: 38.5m²

when rounded to the nearest hundredth: 38.48m²

when rounded to the nearest thousandth: 38.485m²

Step-by-step explanation:

the formula for finding the area of a circle is [tex]A = \pi r^{2}[/tex], where A = area and r = the radius of the circle.

since you're only given the circumference, we need to calculate the radius of the circle before we can find the area.

  • to find the radius of a circle, you can either divide the measure of the diameter by 2 OR use the formula [tex]r=\frac{C}{2\pi}[/tex] where r = radius and C = circumference.
  • because there is no given diameter measurement in your question, the best way to find the radius is to use the formula [tex]r=\frac{C}{2\pi}[/tex].

first, plug the given values into the equation.

since [tex]7\pi[/tex] is the given circumference, plug in [tex]7\pi[/tex] for [tex]C[/tex].

  • [tex]r=\frac{C}{2\pi}[/tex] ⇒ [tex]r=\frac{7\pi}{2\pi}[/tex]
  • the equation becomes [tex]r=\frac{7\pi}{2\pi}[/tex], aka radius equals seven times pi divided by two times pi.

now divide [tex]\frac{7\pi}{2\pi}[/tex].

  • [tex]\frac{7\pi}{2\pi} = 3.5[/tex]

now we know that the radius of the circle is 3.5 :) since we have this information, we can now solve for the area of the circle using the formula [tex]A = \pi r^{2}[/tex].

first, plug in [tex]3.5[/tex] for [tex]r[/tex].

  • [tex]A = \pi r^{2}[/tex] ⇒ [tex]A = \pi 3.5^{2}[/tex]

now multiply [tex]\pi 3.5^2[/tex], aka pi times three and five tenths squared.

  • [tex]\pi 3.5^2 = 38.4845100065[/tex] (if needed, you can round this result to the nearest tenth, hundredth, etc.)

the area of the circle is 38.4845100065m². i hope this helps! have an amazing day <3

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