First, we need to calculate the initial volume of water in the container:
Initial volume = π * (radius)^2 * height
Initial volume = π * (2.5 cm)^2 * 35 cm
Initial volume = π * 6.25 cm^2 * 35 cm
Initial volume = 218.75π cm^3
Next, we need to calculate the final volume of water in the container:
Final volume = initial volume * (1 + β * (final temperature - initial temperature))
Final volume = 218.75π cm^3 * (1 + 457 x 10^-6/°C * (60 °C - 6 °C))
Final volume = 218.75π cm^3 * (1 + 0.026142)
Final volume = 218.75π cm^3 * 1.026142
Final volume = 224.54π cm^3
Now, we can calculate the increase in water level:
Increase in water level = (final volume) / (π * (radius)^2) - 35 cm
Increase in water level = 224.54π cm^3 / (π * 6.25 cm^2) - 35 cm
Increase in water level = 224.54 cm^3 / 6.25 cm^2 - 35 cm
Increase in water level = 35.92768 cm - 35 cm
Increase in water level ≈ 0.93 cm
Therefore, the increase in the water level of the container is approximately 0.93 cm.
Calculate the increase in the water level if a container with a round base, diameter 5 cm, is filled with water up to a level 35 cm from the bottom. The original temperature of the water (6) (5) (2) is 6 °C and the final temperature is 60 °C. The volumetric expansion coefficient of water at 60 °C is 457 x 10-6/°C. Ignore the expansion of the container and determine the increase in the water level.
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