The circumference has increased 6 times. Determine how this will change: a) the diameter of the circle;

The circumference has increased 6 times. Determine how this will change: a) the diameter of the circle; b) the area of the circle.

1. The circumference is: 3.14 * D = L.

2. Let’s designate the initial circumference as L1. In this case, L1 = 3.14 * D1.

3. The circumference has changed and became L2 = 3.14 * D2, as well as L2 = 6 * L1.

4. Then 3.14 * D2 = 6 * 3.14 * D1. D2 = 6 * D1.

5. Area of a circle: S1 = 3.14 * D1 ^ 2/4.

6. After increasing the diameter by a factor of 6: S2 = 3.14 * ((6 * D1) ^ 2) / 4. Area ratio

S2 / S1 = 36.

Answer: a) the diameter has increased 6 times; b) the area has increased 36 times.