Math Lab 1

Math Lab 1: Surface Area to Volume Ratio in Cells

Important Links:

    • Assessments

What's Required for Full Credit (30 pts)

    1. (9 pts) Perform the experiment below. Repeat the experiment twice more after your original run so that you will have done the experiment a total of three times.

    2. (2 pts) Save each repetition on a different Google Spreadsheet Tab (same file, just use multiple sheets (tabs)).

    3. (2 pts) Rename your Google Spreadsheet so that it is titled the same as the title above.

    4. (9 pts) Make a graph for each of your experiments and share the file with your instructor.

    5. (8 pts) Submit the electronic Lab Report.

Introduction

Surface Area-to-Volume Ratio in Cells

Living cells bring in food, water, and oxygen, and excrete wastes through the process of diffusion. diffusion is the movement of molecules across a membrane from an area of higher concentration to an area of lower concentration. In this way, digested food molecules are absorbed into villi in the small intestine, and oxygen moves into and carbon dioxide out of lung cells.

Cells are dependent upon diffusion. They must have an adequate surface area to allow needed molecules in and unwanted molecules out fast enough to sustain their metabolism. A single cell which grows too large will not be able to take in sufficient food and oxygen or eliminate waste molecules fast enough. For this reason, large organisms have to be composed of many small cells.

Finding Volume and Surface Area

Three dimensional objects will have a volume and surface area. Volume is measured in cubic units (cm3) while surface area is measured in square units (cm2).

Object

Rectangular Solid

Sphere

Volume

V = L x W x H

Surface Area

Sum of Areas of all sides

Calculating Surface Area to Volume Ratios

A ratio is the relation of two numbers, and it is used to compare numbers to each other. To find the surface area to volume ratio, make the surface area the numerator and the volume the denominator. Divide the numbers. Note: Ratios are like percentages, they don't have any units with them.

Example: Volume = 40 cm3 and Surface Area = 76 cm2

Equation: SA / V = 76/40 = 1.9

Materials

    • Plastic bags

    • String

    • Metric ruler

    • Graduated cylinder, 100 mL

Procedure

    1. Read the procedure below. Before doing anything, set up a Google Spreadsheet and determine the independent variable and type in that variable in cell 1A. Then determine the dependent variable(s) and type those into cells 1B, 1C and so on.

    2. Fill the corner of a baggie with 100 mL of water. Do not seal it. Hold the baggie so that one corner holds the water.

    3. Measure the circumference (cm) at the widest point with a string and record your value in the Google Spreadsheet.

    4. Fill the corner of a baggie with 200 mL of water. Do not seal it. Hold the baggie so that one corner holds the water.

    5. Measure the circumference (cm) at the widest point with a string and record your value in the Google Spreadsheet.

    6. Fill the corner of a baggie with 300 mL of water. Do not seal it. Hold the baggie so that one corner holds the water.

    7. Measure the circumference (cm) at the widest point with a string and record your value in the Google Spreadsheet.

    8. Fill the corner of a baggie with 400 mL of water. Do not seal it. Hold the baggie so that one corner holds the water.

    9. Measure the circumference (cm) at the widest point with a string and record your value in the Google Spreadsheet.

Analysis

    • Calculate the SA/V ratio for each cell and record