A cylinder with a height of 12, with a base radius of 9 was filled to the top with water. At what level will the water be in another cylinder with a base radius 2 times less than the radius of the first cylinder.
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:
H₁ = 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 in the new vessel will be equal to:
H₂ = 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:
H₂ = 12 * 4 = 48 (cm).
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