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Ther rate of change of the volume is constant. what is happening to the rate at which the water level rises as the volume increases

A) The rate at which the water level rises is increasing.
B) The rate at which the water level rises is decreasing.
C) The rate at which the water level rises remains constant.
D) The rate at which the water level rises is unpredictable.

1 Answer

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Final answer:

The rate at which the water level rises is decreasing when considering a container with a non-uniform cross-section, as each increment of volume will result in lesser increments of water level as the container widens. Option b is the correct answer.

Step-by-step explanation:

When considering the scenario where the rate of change of the volume of water is constant, it implies that the water volume is increasing at a uniform rate over time. Now, the way the water level rises in a container as the volume of water increases will depend on the shape of the container.

If the container has uniform cross-sectional area, such as a cylindrical container, the height of the water (which is the water level) will also increase at a constant rate since the same volume change will result in the same height change regardless of the water level. However, if the container's cross-sectional area expands with height (like a cone or a bowl), the rate at which the water level rises will decrease as the volume increases, because the same volume increment will occupy a larger area and thus result in a smaller rise in level.

The correct option that relates to the rate at which water level rises when the change in volume is constant is therefore option (B): The rate at which the water level rises is decreasing.

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