Answer:
False
Step-by-step explanation:
Circumference(C) and Area(A) of the circle is given by:
[tex]C = 2 \pi r[/tex]
[tex]A = \pi r^2[/tex]
where, r is the radius of the circle.
As per the statement:
A circle with circumference of 10 has area of 100.
Circumference = 10 units
then;
[tex]2 \pi r = 10[/tex]
Divide both sides by [tex]2 \pi[/tex] we have;
[tex]r = \frac{5}{\pi}[/tex] units
Find area of circle:
[tex]A = \pi r^2[/tex]
Substitute the value of r we have;
[tex]A = \pi \cdot (\frac{5}{\pi})^2[/tex]
⇒[tex]A = \pi \cdot \frac{25}{\pi^2} = \frac{25}{\pi}[/tex]
But A = 100 square units
⇒[tex]A = \frac{25}{\pi} \neq 100[/tex]
Therefore, the given statement is FALSE
