if the circumference of circle is 40% of its area then what is the area of the circle?
if the circumference of circle is 40% of its area then what is the area of the circle?
Answer: Let’s assume that the radius of the circle is ‘r’.
The circumference of a circle can be given by the formula:
C = 2πr
And the area of a circle can be given by the formula:
A = πr^2
According to the given information, the circumference of the circle is 40% of its area. Mathematically, we can write this as:
C = 0.4A
Substituting the formulas for C and A, we get:
2πr = 0.4πr^2
Dividing both sides by πr, we get:
2/r = 0.4
Simplifying this equation, we get:
r = 5
Therefore, the radius of the circle is 5 units.
Using the formula for the area of a circle, we can find the area as:
A = πr^2
= π(5)^2
= 25π
Therefore, the area of the circle is 25π square units.