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Graphs in Practical Situations

Graphs in Practical Situations

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The diagram below shows an empty container made up of a cylinder and a cone.

The cylinder and the cone both have radius \(4\) cm and height \(7\) cm.

  1. Find the volume of the container leaving your answer in terms of \(\pi \).
  2. It takes \(56\) s to fill up the entire container.
    Find the time taken to fill up the cone.
  3. Water is poured into the container at a constant rate. Using the axes below, sketch the graph showing how the height of water in the container varies over the \(56\) seconds.

Solution:

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Answer:Volume \(448\pi/3\text{ cm}^3\); cone fills in 14 s; height rises with decreasing gradient to \((14,7)\), then linearly to \((56,14)\).

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