Size and Shapes of Cells: Surface Area:Volume Ratios

[Adapted from Cohen, Annette, Moreh, Anat Ben, & Chayoth, Reuben. (1999, November/December). Hands-on method for teaching the concept of the ratio between surface area &volume. The American Biology Teacher 61(9), 691-695.]

1. Count out 27 plastic cubes. The dimensions of each cube are 1 centimeter (cm) X 1 cm x 1 cm.

2. Examine a single cube. (KEEP THIS CUBE SEPARATE)

A. What is its surface area?

B. What is its volume?

C. What is its surface area:volume ratio?

3. Make a cube that is 2 cm x 2 cm X 2 cm. (KEEP THIS CUBE SEPARATE)

A. What is its surface area?

B. What is its volume?

C. What is its surface area: volume ratio?

4. Make a cube that is 3 cm x 3 cm X 3 cm. (KEEP THIS CUBE SEPARATE)

A. What is its surface area?

B. What is its volume?

C. What is its surface area: volume ratio?

5. Compare the ratios you obtained in the progressively larger cubes.

6. Look at the three cubes you have constructed. If these represented the sizes of three different living cells, how would the size of the cells affect their functioning?

7. Using just 24 of your smallest cubes, produce a larger structure that is 4 cm long, 3 cm wide, and 2 cm high.

A. What is its surface area?

B. What is its volume?

C. What is its surface area: volume ratio?

D. What type of cell might this shape represent?

8. Using the same 24 cubes, produce a structure that is 8 cm long, 3 cm wide, and 1 cm high.

A. What is its surface area?

B. What is its volume?

C. What is its surface area: volume ratio?

D. What type of cell might this shape represent?

9. Using the same 24 cubes, produce a structure with the surface area of 98 cm2.

A. What is its volume?

B. What is its surface area: volume ratio?

C. What type of cell might this shape represent?

10. Which of the shapes you produced in 7, 8, and 9 would be the most efficient for an especially active (metabolically) cell?

11. Using the 4 X 3 X 2 cube you made in #7 above, rearrange the blocks in a way that increases the surface area while keeping the volume constant.

A. Draw the shape of the model you produced.

B. What is its surface area?

C. What is its volume?

D. What is its surface area: volume ratio?

E. What type of cell might this shape represent?

12. Imagine that you have recently eaten a cheeseburger. Large globules of fat have left your stomach and entered your small intestine. The pancreas then releases an enzyme (pancreatic lipase) into the small intestine which can break down the lipids into molecules small enough to be absorbed into the intestinal cells. Bile is a substance produced by the liver and also released into the small intestine in response to the presence of the fat. The function of the bile is to increase the surface area of the fat globule so that the pancreatic enzymes can work on it more effectively.

A. Once again make a cube that is 4 cm long, 3 cm wide, and 2 cm high (#11 above) and this time imagine that it is a fat globule.

i. What is its surface area? (See your calculations from #7 above.)

ii. What is its volume?

iii. What is its surface area: volume ratio?

B. What could the bile do to the fat globule to greatly increase its surface area?

i. Rearrange the blocks to show this and draw what you have done to the fat globule.

ii. Now what is the surface area?

iii. Now what is the volume?

iv. Now what is the surface area to volume ratio?

v. How would these changes affect the digestion oflipids?