7.2: Procedure

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The instructor will provide everybody with two differently colored Plasticizoans and a ruler.

Shape them, as instructed, into cylinders, one about 30 mm in height (“Short”), and another about 70 mm in height (“Tall”). Do your best to make the ends as flat as possible, and the circumference equal throughout each organism.
Measure them with a ruler: height (\(h\)) in mm, and diameter (\(d\)) which is a distance across the cylinder’s base, also in mm. Record this data.
Convert diameter into radius (\(r\)) by dividing diameter by 2: \(d=2r\) so \(r=\frac{d}{2}\). Record the radius.
Now, calculate volume and surface area for each of the two organisms.

Formulas for the cylinder:

to calculate volume, use

\[V=\pi r^2 h\]

and to calculate surface, use

\[A=2\pi r h + 2\pi r^2\]
Calculate the relative surface area (a.k.a surface area to volume ratio):

\[R=A/V\]
Now, transform your short cylinder to make the relative surface as small as possible. This will decrease contact with the environment. What shape is it now?

... Yes, it is a sphere! This shape has the absolute lowest surface area to volume ratio possible. As in, it has the very least contact with the environment.
As before, measure the radius. To do so, you will have to cut the sphere in half with your scalpel, measure the diameter, and divide by two. Record the diameter and radius.
Calculate volume, surface area, and relative surface area for the Spheric plasticizoan.

Formulas for the sphere:

to calculate volume of sphere, use

\[V=\frac{4}{3}\pi r^3\]

and to calculate surface of sphere, use

\[A=4\pi r^2\]
We transformed the short cylinder, which started out with a high surface area to volume ratio, into a sphere, which had a low surface area to volume ratio. We therefore reduced the contact with the environment.

Now, modify your Tall into another shape that has a really high surface area to volume ratio, the highest ratio you can achieve, to increase the contact with the environment.

What might this shape be? Show your new animal to instructor.