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A farmer has an underground water tank which he decided to calibrate by adding known volumes of water and measuring the depth using a dip-stick. His calibration graph is shown The horizontal cross section of the tank is circular at all points.

1. Which one of the following shows a possible vertical cross sectional shape of the tank?
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    Explanation

    The correct answer is E.

    Initially, the gradient of the graph is increasing, which means there is an increasingly greater change in depth per unit change in volume. This means the width of the tank must be decreasing from the bottom. The gradient of the graph then decreases as we fill to the the top of the tank, which means there is a smaller change in depth per unit change in volume, so the tank must be getting narrower. Only E shows the tank getting narrower and then wider (from bottom to top), so this must be the answer.

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