edited by
Robert Panoff
published by
the Shodor Foundation
supported by
the National Science Foundation

This Java-based activity lets students manipulate a 3-D rectangular prism or triangular prism to explore surface area and volume. The geometric model is designed to help secondary students visualize the relationship of width, depth, and height in calculating and estimating volume/surface area.

This resource is part of CSERD (Computational Science Education Reference Desk), a portal of the National Science Digital Library. The Interactivate collection contains more than 200 standards-based activities, many of which have been classroom tested.

Please note that this resource requires
Java Applet Plug-in.

6-8: 9C/M7. For regularly shaped objects, relationships exist between the linear dimensions, surface area, and volume.

6-8: 9C/M10. Geometric relationships can be described using symbolic equations.

9-12: 9C/H2. When the linear dimensions of an object change by some factor, its area and volume change disproportionately: area in proportion to the square of the factor and volume in proportion to its cube. Properties of an object that depend on its area or volume also change disproportionately.

11. Common Themes

11B. Models

6-8: 11B/M4. Simulations are often useful in modeling events and processes.

9-12: 11B/H3. The usefulness of a model can be tested by comparing its predictions to actual observations in the real world. But a close match does not necessarily mean that other models would not work equally well or better.

Common Core State Standards for Mathematics Alignments

Standards for Mathematical Practice (K-12)

MP.4 Model with mathematics.

Measurement and Data (K-5)

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. (5)

5.MD.3.a A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume.

5.MD.5.a Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

5.MD.5.b Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

This resource is part of a Physics Front Topical Unit.

Topic: Measurement and the Language of Physics Unit Title: Applying Measurement in Physics

This Java-based activity lets students manipulate a 3-D rectangular prism or triangular prism to explore surface area and volume. It's designed to help secondary students visualize the relationship of width, depth, and height in calculating and estimating volume/surface area.

CSERD Interactivate: Surface Area and Volume, , edited by R. Panoff (Shodor Foundation, Durham, 2006), <http://www.shodor.org/interactivate/activities/SurfaceAreaAndVolume/>.

Panoff, R. (Ed.). (2008, June 29). CSERD Interactivate: Surface Area and Volume. Retrieved December 1, 2015, from Shodor Foundation: http://www.shodor.org/interactivate/activities/SurfaceAreaAndVolume/

Panoff, Robert, ed. CSERD Interactivate: Surface Area and Volume. Durham: Shodor Foundation, June 29, 2008. http://www.shodor.org/interactivate/activities/SurfaceAreaAndVolume/ (accessed 1 December 2015).

@misc{
Title = {CSERD Interactivate: Surface Area and Volume},
Publisher = {Shodor Foundation},
Volume = {2015},
Number = {1 December 2015},
Month = {June 29, 2008},
Year = {2006}
}

%A Robert Panoff, (ed) %T CSERD Interactivate: Surface Area and Volume %D June 29, 2008 %I Shodor Foundation %C Durham %U http://www.shodor.org/interactivate/activities/SurfaceAreaAndVolume/ %O application/java

%0 Electronic Source %D June 29, 2008 %T CSERD Interactivate: Surface Area and Volume %E Panoff, Robert %I Shodor Foundation %V 2015 %N 1 December 2015 %8 June 29, 2008 %9 application/java %U http://www.shodor.org/interactivate/activities/SurfaceAreaAndVolume/

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This is a very simple Java applet in which students fill a box with cubes, layer upon layer, to visualize how volume is calculated in a rectangular prism.

This is a simpler version of volume in rectangular prisms. Students manipulate two solid rectangles (shown side-by-side) to see the effect that even a small change in length/width will have on volume. Values are computed automatically in this applet.

This standards-based lesson for grades 6-8 lets students calculate and compare volumes of cylinders and rectangular prisms using bales of hay as the common unit.