Surface Area and Volume

(Modified from Washington MESA Packaging and the Environment Curriculum)

More is Less

Activity Objectives

Students will increase their understanding of the relationship between surface area and volume. They will also explore environmentally sound methods of packaging.

Activity 1 Directions

  1. Build a 4 x 4 x 4 unit cube. Calculate the surface area and volume of the cube and record your results in the table below.
     
  2. Slide a 2 x 4 x 4 section of the large cube and realign it with the remaining section to form another rectangular solid. Record the dimensions in the table.
     
  3. Calculate and record the surface area and volume of this new rectangular solid in the table.
    Dimensions Surface Area in Square Units Volume in Cubic Units
    4 x 4 x 4     
         
  4. How do the surface area and volume of the new solid compare with the surface area and volume of the 4 x 4 x 4 unit cube? Explain.

Activity 2 Directions

  1. Using the manipulatives provided, build the following unit cubes to complete the table below.
    Unit Cube Size Surface Area in Square Units Volume in Cubic Units
    1 x 1 x 1    
    2 x 2 x 2    
    4 x 4 x 4    
    8 x 8 x 8     
  2. Based on these results, write a conclusion that describes what happens to the surface area and volume of a cube when you double the length of each side.