The height of a straight cone is 5 times less than the generatrix and the radius of settling is 2√30, find the volume.

Since we know the radius of the base and the ratio between the height and the generatrix, and since these three line segments form a right-angled triangle, so the Pythagorean theorem applies. Let’s denote the height by x, then the generatrix is 5x. We get:

(5x) ^ 2 = x ^ 2 + (2√30) ^ 2

25x ^ 2 = x ^ 2 + 120,

24x ^ 2 = 120,

x ^ 2 = 5,

x = √5. A negative root is not suitable for solving the problem.

To calculate the volume, we use the ratio: V = 1/3 S h = 1/3 πr2h. We calculate the volume of the cone:

1/3 * 3.14 * (2√30) 2 * √5 = 1/3 * 3.14 * 120 * √5 = 280.85.

Answer: The volume of the pattern is 280.85.