NRICH: Fill Me Up

Can you sketch graphs to show how the height of water changes in different containers as they are filled?

Below are some images of containers. Imagine you put them under a steady stream of water.

What would the graphs look like if you plotted the height of the water level against the volume of water as the containers fill up?

Draw a sketch graph for each container. You will need to consider which portions of each graph will be straight and which will be curved. Can you suggest suitable units and scales for the axes?
 

Beaker
 
Conical flask
 
Boiling tube
 
Round-bottomed flask
 
Pint glass
 
Volumetric flask

 

Once you have sketched the graphs, you might like to plot the graphs by collecting some data.

One way to do this is to collect suitable containers, add water in fixed amounts and measure the height at each stage. Do your experimental graphs match your sketches?
Age 11 to 14


Algebra & Pre-Algebra, Functions & Graphs
Middle School, High School, Educator

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