Answer:
False
Step-by-step explanation:
Circumference(C) and Area(A) of the circle is given by:
\(C = 2 \pi r\)
\(A = \pi r^2\)
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;
\(2 \pi r = 10\)
Divide both sides by \(2 \pi\) we have;
\(r = \frac{5}{\pi}\) units
Find area of circle:
\(A = \pi r^2\)
Substitute the value of r we have;
\(A = \pi \cdot (\frac{5}{\pi})^2\)
⇒\(A = \pi \cdot \frac{25}{\pi^2} = \frac{25}{\pi}\)
But A = 100 square units
⇒\(A = \frac{25}{\pi}
eq 100\)
Therefore, the given statement is FALSE
