# Surface Area to Volume Ratio Activities

Instructor: Heather Jenkins

Heather has a bachelor's degree in elementary education and a master's degree in special education. She was a public school teacher and administrator for 11 years.

If your class is studying shapes in three dimensions, consider having students learn how to calculate the surface area to volume ratios for different 3-D shapes. Use these activities to help students understand surface area to volume ratio.

## SA:V

In chemistry and biology, calculating the surface-area-to-volume ratio helps scientists know how fast a chemical will dissolve or how materials will move in and out of a cell.

When students learn how to calculate the surface-area-to-volume ratio, it helps them to understand how much area they can see for every unit of volume in a solid shape. Students can gain more a in depth understanding of surface area and volume and how they relate to each other in different 3-D shapes.

Let's look at some activities to help students calculate surface-area-to-volume ratio.

## Compare the Shapes

Have student calculate the surface-area-to-volume ratio for different cube shaped boxes and Styrofoam spheres.

### Materials

• Cube-shaped boxes (various sizes)
• Styrofoam spheres (various sizes, cut in half)
• Rulers
• Paper
• Pencils

### Teacher Directions

• Show students how to calculate the surface-area-to-volume ratios for cubes and spheres. Model how to calculate this ratio by finding the surface area and dividing it by the volume and how to find the ratio with the simplified version of the formulas (6/side for a square and 3/radius for a sphere).
• Show students a cube-shaped box (such as tissue box) and a Styrofoam sphere. Demonstrate how to measure the sides of the box and how to measure the radius of the sphere using one of the hemispheres. Then, model how to use these measurements to find the shapes' surface area to volume ratios.
• Divide the class into pairs and provide each pair with rulers, pencils, paper, several cube-shaped boxes in various sizes, and several Styrofoam spheres in various sizes.
• Have students calculate the surface-area-to-volume ratio for each shape.

### Discussion Questions

• How did the size of the shape compare to the surface-area-to-volume ratio? Did seemingly bigger shapes have larger ratios?
• How did a large surface area affect the surface-area-to-volume ratio? How did a large volume affect the ratio?
• Did the cubes or spheres seem to have a larger surface-area-to-volume ratio? Why do you think this occurred?

## Marshmallow Shapes

Engage students in using marshmallows and toothpicks to create cubes with specific surface-area-to-volume ratios.

### Materials

• Mini marshmallows
• Toothpicks
• Rulers
• Dry-erase boards
• Dry-erase markers

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