Fill Me Up

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

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem

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
Image
Fill Me Up



 

Conical flask
Image
Fill Me Up



 

Boiling tube
Image
Fill Me Up



 

Round-bottomed flask
Image
Fill Me Up



 

Pint glass
Image
Fill Me Up
Volumetric flask
Image
Fill Me Up

 

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