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Fill Me Up

Age 11 to 14
Challenge Level Yellow starYellow star
Secondary curriculum
  • Problem
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Fill Me Up printable sheet
 

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?
 


Pictures
 
http://commons.wikimedia.org/wiki/File:Becher-pyrex-150mL.jpg
http://commons.wikimedia.org/wiki/File:Pyrex_Conical_Flask.jpg
http://commons.wikimedia.org/wiki/File:Pint_glass_300x509.jpg
http://commons.wikimedia.org/wiki/File:Volumetric_flask_hg.jpg
Thanks to Euan Willder for the pictures of the Boiling Tube and Round Bottomed Flask

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  • Functions and Graphs - Stage 3

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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