The diameter of the circle was doubled, how will the area of the circle change?

To get the area of a circle, it is enough to know the radius of the circle. The area itself is obtained by multiplying the square of the radius by the constant pi. S = n * r ^ 2.

Let the area be equal to S1 = n * r1 ^ 2 before increasing the diameter.

The diameter has doubled. D2 = 2 * D1.

Lengthwise diameter is equal to two radii. 2 * r ^ 2 = 2 * 2 * r1. r ^ 2 = 2 * r1.

New area of the circle: S2 = n * r2 ^ 2 = n * (2 * r1) ^ 2 = 4 * n * r1 ^ 2.

As you can see, the area of the circle will quadruple.