# SURFACE AREA TO VOLUME RATIO by lindahy

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INTRODUCTION
A knowledge of the relationship between the size of cells and their surface area helps us explain many
aspects of cell functioning. A model of a cell is used to simplify these studies.

Background Information
A scientific model is a simplified representation of a more complex phenomenon. Models are used to
increase understanding and make predictions. The limitations of the model are:
•	 Volume is the amount of space occupied by an object. Volume is expressed in cubic units (cm3,
m3).
•	 Surface area is the area covering the surface of any object. Surface area is expressed in square
units (cm2, m2).
•	 Surface area to volume ratio (SA/V) refers to the number of units of surface area possessed by an
object for each unit of volume. The ratio is calculated by dividing the surface area by the volume.
Units are expressed as cm2/cm3 or m2/m3.
•	 Phenolphthalein is a chemical indicator that is dark red in the presence of a base (sodium
hydroxide) and colourless in an acid (hydrochloric acid).

PURPOSE
To use a model to investigate the effect of:
A. size on SA/V ratio
B. shape on SA/V ratio
C. SA/V ratio on the rate of diffusion into an object.

REQUIREMENTS (PER GROUP)
•	 Agar-phenolphthalein –sodium hydroxide jelly at least 4 cm thick and cut into 3 different cubes
with sides of 3 cm, 2 cm, and 1 cm.
•	 0.1 M hydrochloric acid (approximately 100mL)
•	 Ruler (marked in cm and mm)
•	 Paper towel
•	 Beaker (250 mL)
•	 Plastic spoon

Original Source: “Core Biology Practical”, Ed by Mudie and Brotherton, Sofima
Productions,	Sydney,	1984

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PROCEDURE A­ - EFFECT OF SIZE
•	 Take 3 different size cubes.
•	 Calculate the Surface area, volume and SA/V ratio for each cube.
•	 Record in a table.

PROCEDURE B – EFFECT OF SHA­PE
•	 Take models of the 4 shapes listed below. If you use the dimensions given, they will all have the
same volume.
•	 Calculate the SA/V ratio for each shape and complete the table.

Shape          Volume      Dimensions             Volume     SA           SA         SA/V
Formula                                       Formula
Sphere                     Radius = 1.86 cm       27 cm3
Diameter = 3.7 cm
Cylinder                   Radius = 1.7 cm        27 cm3
Diameter = 3.4 cm
Height = 3 cm
Cube                       Side = 3 cm            27 cm3

Sheet                      Length = 9 cm          27 cm3
Height = 1 cm

PROCEDURE C – RA­TE IF DIFFUSION
•	 Place the 3 cubes from Procedure A in a beaker. Cover with the hydrochloric acid and leave for 10
minutes. Turn over every 2 minutes. (DO NOT use your fingers. Use the spoon.)
•	 Remove from acid. Quickly blot dry with paper towel. Cut in two and measure the rate of
penetration of the acid in each cube.
•	 Record results in table and complete the calculations.

Cube side      Volume    SA/V       Depth of       Volume left    Percentage still   Percentage
V                    Penetration    coloured VC    coloured C%        penetrated P%
(Vc/V x 100)       (100 – C%)
3 cm
2 cm
1 cm

Original Source: “Core Biology Practical”, Ed by Mudie and Brotherton, Sofima
Productions,	Sydney,	1984

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DISCUSSION

1. State in words:
a. the effect of size on SA/V ratio;
b. the effect of shape on SA/V ratio.

2. What is the effect of SA/V ratio on the rate of diffusion into an object?

3. What is the significance of these results for living cells?

4. Describe another example where SA/V ratio has an important role to play.

5. What re the main limitations of the jelly models?

Further Investigation

Repeat Procedure C using different shaped solids. Record observations and discuss your results.

Design an experiment to discover the relationship between SA/V ratio and diffusion over time.

Original Source: “Core Biology Practical”, Ed by Mudie and Brotherton, Sofima
Productions,	Sydney,	1984

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