Questions: The figure to the right shows a container that is to be filled with water from the top. Assume that water is poured into the container at a constant rate and the container is filled in 10 s. Assume also that the horizontal cross sections of the container are always circles. Let h(t) be the depth of the water in the container at time t, for 0 ≤ t ≤ 10. Complete parts (a) through (d) below. a. Sketch a graph of the function y=h(t), for 0 ≤ t ≤ 10. Choose the correct graph below. A. B. C. D.

Solution Steps

The problem involves a container being filled with water at a constant rate over 10 seconds. The container has horizontal cross-sections that are always circles. We need to sketch a graph of the function \( y = h(t) \), where \( h(t) \) is the depth of the water in the container at time \( t \).

The container appears to be spherical. As water is poured into a spherical container at a constant rate, the depth of the water will not increase linearly because the cross-sectional area changes with depth.

Given that the container is spherical:

• At the beginning, the depth increases slowly because the cross-sectional area is small.
• As the depth increases, the cross-sectional area increases, causing the depth to increase more rapidly.
• Near the top, the cross-sectional area decreases again, causing the depth to increase more slowly.

Final Answer