Final answer:
The statement 'a circle with circumference of 10 has area of 100' is false.
Step-by-step explanation:
The statement 'a circle with circumference of 10 has area of 100' is false.
The area of a circle is given by the formula A = πr², where π is approximately 3.14159 and r is the radius of the circle. In this case, we are given the circumference of the circle, not the radius.
However, we can calculate the radius using the formula circumference = 2πr. Plugging in the given circumference of 10, we get 10 = 2πr.
Solving for r, we get r = 10/(2π).
Now we can calculate the area by using the formula A = πr², where r is the radius we just calculated. The area is approximately 15.915.
Therefore, the area of a circle with circumference of 10 is not 100, but approximately 15.915.