Key concepts
Mathematics
Geometry
Three-dimensional
Volume

Introduction
Have you ever had fun making different figures or colorful shapes out of Play-Doh? You can squish and stretch a single piece of Play-Doh to make all sorts of shapes. How does changing the shape affect its volume? In this science activity you will find out by investigating how a piece of clay's shape affects its dimensions (length, width and height) as well as how these changes are related to its volume.

Background
Geometry is the study of how to use math to describe and investigate different points, lines and shapes. A very basic three-dimensional shape is the rectangular prism, which is the shape of a box or a book; it has six sides. If all six sides are the same size and perfectly square, such as with dice, it is a cube. Areas and volumes of cubes and rectangular prisms can be measured with the same geometrical formulas.

Mathematical formulas describe geometrical shapes and are a way to calculate different properties of an object, such as its area and volume. Volume is a unique property of three-dimensional shapes because these shapes take up space in three different directions: length, width and height. In this science activity you will use Play-Doh (or homemade clay) to make a model of a rectangular prism, change one of its dimensions (height) and see what effect this has on the other two dimensions as well as the object's volume.

Materials

• Play-Doh (Alternatively, you can prepare homemade salt dough using plain flour, table salt, water and other optional ingredients; see the "Preparation" section for details. Optional ingredients include vegetable oil, wallpaper paste and lemon juice.)
• Permanent marker
• Ruler
• A table or desk
• A flat surface, such as a hard binder or book
• A scrap piece of paper and a pen or pencil

Preparation
• If you want to make homemade salt dough, mix together two cups of plain flour, one cup of table salt and one cup of water. Optional ingredients include one tablespoon (tbsp.) of vegetable oil (to make it a little easier to knead), one tbsp. of wallpaper paste (to give the mixture more elasticity) and/or one tbsp. of lemon juice (to make the finished product harder).

Procedure
• Remove a chunk of dough about as large as your fist. Make your dough into a cube shape, approximately square on all sides.
• Using a permanent marker, label each of the three dimensions of the cube with a "W" (for "width"), "L" (for "length") and "H" (for height). On either side of each letter put a dash to show the direction of the dimension on that side of the cube.
• Place your labeled cube of dough on a table or desk with the side marked for height pointing up and down (the dashes should be vertical). Use a ruler to measure the three dimensions you labeled on the cube (length, width and height). What are the measurements of the cube? Write these down on a sheet of paper.
• Now you are ready to change the shape of your dough by squishing it. Put a flat surface, such as a book or a hard binder, on top of the dough cube. Slowly press down on the dough while keeping the corners square (straight) as you go by patting in from the sides with your hands. Stop pressing down when it looks like the dough has changed shape a little. How does the dough look now? What shape is it?
• Again use a ruler to measure the three dimensions you labeled on the dough. What are the measurements of the dough now? Write these down.
• Again squish the dough as you did before, trying to keep the corners square, and stop pressing down when the dough has visibly changed shape again. How does the dough look this time?
• Use a ruler one more time to measure the three dimensions you labeled on the dough. What are the measurements of the dough this last time? Write these down.
• For each time you measured the dough, multiply its length by width by height to calculate the volume of the shape in centimeters cubed. What was the volume of the shape each time you squished the dough?
• Overall, what happens as one dimension (the one you flattened) decreases? Do the other two dimensions increase or decrease? Does changing the dimensions of the dough affect its volume or does the volume stay the same?
• Extra: In this activity you changed the length, width and height of a cube of dough but you did not change the amount of dough you used. What would happen if the amount of dough did change? Would the volume also change? Try this activity again but this time add or take away some dough and form the dough into a cube, and measure the dimensions of the shape.
• Extra: You could take your results from this activity and graph them. A good type of graph to use for this activity is a bar graph. Looking at your graph, how do the dimensions and volume change as the shape of the dough changes?

Observations and results
As you squished the cube of dough, did its height get smaller, its width and length get larger and its volume stay the same?

In this activity, because the amount of dough used did not change (you did not add dough or take any away), the size, or volume, of the dough should have stayed the same. Because the mathematical formula for calculating the volume of a cube is length X width X height and the volume stayed the same, as you squished the cube its height should have decreased (the cube was being flattened) whereas its length and width increased. For example, the initial cube may have had a length, width and height each equal to four centimeters. As the cube became squished, this may have changed to a length of five centimeters, a width of five centimeters and a height of 2.6 centimeters. Although the shape of the dough changed, its volume remained the same (each of these shapes have a volume of approximately 65 cubic centimeters).

More to explore
Cube, from Coolmath.com
Definition of Volume, by MathIsFun.com
Play-Doh Math, from Science Buddies
Science Activities for All Ages!, from Science Buddies

This activity brought to you in partnership with Science Buddies