Answer:
[tex]50.2 cm^2[/tex]
Explanation:
Here we want to find the largest area of a circle that can be made from a piece of thread 25.2 cm long, assume no knot .
This means that the circumference of the circle must equal to the length of the thread, so we can write:
L = 25.2 cm
And the circumference can be written as:
[tex]2\pi r = L = 25.2[/tex]
where
r is the radius of the circle
Solving for r, we find the radius:
[tex]r=\frac{L}{2\pi}=\frac{25.2}{2\pi}=4.0 cm[/tex]
The area of a circle is given by the formula
[tex]A=\pi r^2[/tex]
So in this case, we find:
[tex]A=\pi (4.0)^2=50.2 cm^2[/tex]
