Discover new knowledge and insights with IDNLearn.com's extensive Q&A database. Get comprehensive answers to all your questions from our network of experienced experts.

The circumference of a circle is 13π ft. What is the area, in square feet? Express your answer in terms of piπ.

Sagot :

Answer:

[tex]\boxed{A=\dfrac{169}{4}\pi\ \text{ ft}^2}[/tex]

Step-by-step explanation:

We know the following formulas regarding circles:

  • [tex]C=2\pi r[/tex]
  • [tex]A=\pi r^2[/tex]

where [tex]r[/tex] is the circle's radius and [tex]\pi[/tex] is a constant [tex]\approx 3.14159[/tex].

We are given the circumference of a circle:

  • [tex]C=13\pi[/tex]

Plugging this into the first equation, we can solve for r:

[tex]13\pi = 2\pi r[/tex]

↓ dividing both sides by [tex]2\pi[/tex]

[tex]\dfrac{13}{2} = r[/tex]

We can now solve for area using this r-value:

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

[tex]A=\pi (13/2)^2[/tex]

[tex]\boxed{A=\dfrac{169}{4}\pi\ \text{ ft}^2}[/tex]

Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Find the answers you need at IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.