desireewilliamson177
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Henry knows that the circumstance of a circle is 18pi inches. What is the area of the circle?

a. 36pi in²
b. 81pi in²
c. 162pi in²
d. 324pi in²​

Sagot :

igoroleshko156

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Answer:  [tex]\textsf{Option B, 81}\pi\textsf{ in}^2[/tex]

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Given: [tex]\textsf{Circumference = 18}\pi[/tex]

Find:  [tex]\textsf{The area of the circle}[/tex]

Solution:  We need to first determine the radius using the circumference formula and once we get the radius then we can plug in the value into the area formula and get our final answer.

Determine the radius

  • [tex]c = 2 \pi * r[/tex]
  • [tex]18\pi = 2 \pi * r[/tex]
  • [tex]\frac{18\pi}{2\pi} = \frac{2 \pi}{2\pi} * r[/tex]
  • [tex]\frac{18\pi}{2\pi} = r[/tex]
  • [tex]9 = r[/tex]

Determine the area

  • [tex]A = \pi * r^2[/tex]
  • [tex]A = \pi * (9)^2[/tex]
  • [tex]A = \pi * (9 * 9)[/tex]
  • [tex]A = 81\pi[/tex]

Therefore, the correct answer would be option B, 81π in2.

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