The water level in a cylindrical vessel reaches 15cm. What level will the water reach if it is poured

The water level in a cylindrical vessel reaches 15cm. What level will the water reach if it is poured into another similar vessel, whose base radius is 2 times less than that of the first?

The volume of water in a cylindrical vessel can be found by the formula:

V = π * R² * H,

where R is the radius of the cylinder base, H is the water level.

We find H by proportion:

H = V / (π * R²).

According to the condition, the water was poured into a cylindrical vessel, the base radius of which is 2 times smaller, then the water level will be equal to:

H = V / (π * (R / 2) ²) = V / (π * R² / 4) = V: (π * R²) / 4 = (4 * V) / (π * R²).

To find how many times the water level in the second vessel has changed compared to the first, it is necessary to divide the water level in the second vessel by the water level in the first vessel:

(4 * V) / (π * R²): V / (π * R²) = (4 * V) / (π * R²) * (π * R²) / V = ​​(reduce fractions) = 4.

Thus, the water level in the second vessel is 4 times higher than the water level in the first vessel: H = 15 * 4 = 60 (cm).

Answer: H = 60 cm.