Answered

Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Find the diameter of the circle that has a circumference equal to its area.

2
4
8
10

Sagot :

naǫ
The formula for circumference of a circle:
[tex]C=2 \pi r[/tex]

The formula for area of a circle:
[tex]A=\pi r^2[/tex]
r - radius

The circumference is equal to the area.
[tex]C=A \\ 2 \pi r=\pi r^2 \ \ \ |\div \pi r, \ r>0 \\ 2=r \\ r=2[/tex]

The diameter is two times the radius.
[tex]d=2r=2 \times 2=4 \\ \\ \boxed{d=4}[/tex]
AL2006

Circumference may have the same numerical magnitude as area, but they will never be "equal".  Circumference is a length or distance, and area is an area.
So they can never have the same units, and quantities can't be equal without
the same units.

You might say that   π D (circumference) = π (D/2)²  (area) .

Then  D = (D/2)²

           D = D² / 4

           1 = D / 4

           D = 4 .

But this is no more than a parlor trick.  In order to do it, you need to
ignore units completely, and that's unacceptable in math.


Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.