The volume of the cylinder was 36 dm3, the height was increased by 3 times, and the radius of the base was

The volume of the cylinder was 36 dm3, the height was increased by 3 times, and the radius of the base was decreased by 3 times. What is the volume of a new cylinder?

1. Trigonometric formula for calculating the volume of a cylinder:

V = S base * height.

2. By the condition of the problem, it is known that the initial volume of the cylinder is 36 dm³.

3. Substitute the given values into the general formula and get

36 dm³ = п * R² * H.

If we change the parameters of the cylinder so that H2 = 3 H, and R2 = 1/3 R, then we get

V2 = п * R2² * H2 = п * (1/3 R) ² * 3 H = п * 1/9 R² * 3 H = 1/3 п R² H = 1/3 V.

That is, the new V2 = 1/3 * 36 dm³ = 12 dm³.

Answer: The volume of the newly obtained cylinder is 12 dm³.