Find the area of a circle if four-ninths of the circumference of this circle is 49.6 cm.

1. When calculating, we use the formulas:

a) the circumference is 2 * P * r;

b) the area of the circle is equal to P * R².

2. By the statement of the problem, it is known that the value of 4/9 of the circumference is 49.6 cm.

Let’s calculate the entire length of a circle L according to the rule: to find a number by its part, we must divide a part of the number by a fraction expressing this part.

L = 49.6 cm: 4/9 = 49.6 cm * 9/4 = 111.6 cm.

Then r = L: 2 P = 111.6 cm: 6.2 = 18 cm.

3. Determine the value of the area of the circle

S = 3.1 * 18² = 3.1 * 324 cm² = 1004.4 cm².

Answer: The area is 1004.4 cm².