4.2: Why Are Cells Small? (Activity)
- Page ID
- 24759
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Introduction
- Take 3 blocks of agar of different size (1cm, 2cm, 3cm) → these are our cell models.
- Measure the length, width, and height of each cube using a ruler.
- Calculate the area of each face of the cubes and add all the areas together for a single cube.
- A cube has 6 faces → the total surface area is the same as the area of one side multiplied by 6.
- Calculate the volume of each cube.
- Report the surface area-to-volume in the table below.
Data Table: Calculating Surface Area-to-Volume Ratio
|
Cell Model (Cube) |
Length |
Width |
Height |
Total Surface Area |
Volume of cell |
Surface Area: Volume |
|
1 |
||||||
|
2 |
||||||
|
3 |
Stop and Think
- Which cube has the greatest surface area:volume ratio?
- Which cube has the smallest surface area:volume ratio?
- Hypothesize: In an osmosis or diffusion experiment, which cube size would have the greatest diffusion rate?
Procedures
- Each group will acquire three agar cubes: A 3cm cube, a 2cm cube, and a 1cm cube. CUT AS ACCURATELY AS POSSIBLE. (This may be already completed for you.)
- Place cubes into a beaker and submerge with 200 ml NaOH.
- Let the cubes soak for approximately 10 minutes.
- Periodically, gently stir the solution, or turn the cubes over.
- After 10 minutes, remove the NaOH solution.
- Blot the cubes with a paper towel.
- Promptly cut each cube in half and measure the depth to which the pink color has penetrated. Sketch each block’s cross-section.
- Record the volume that has remained white in color.
- Do the following calculations for each cube and complete the following data table:
Data Table: Calculation of Diffusion Area-to-Volume
|
Cube Size |
Cube volume (cm3) (Vtotal) |
Volume white (cm3) (Vwhite) |
Sketch of each Cube |
Volume of the diffused cube ( Vtotal – Vwhite ) = (Vdiffused) |
Percent Diffusion (Vdiffused/Vtotal) |
Surface Area: Volume (from the previous table) |
| 1 cm. | ||||||
| 2 cm. | ||||||
| 3 cm. |
Conclude
1. Which cube had the greatest percentage of diffusion?
2. Did this meet your expectations with your hypothesis?
3. If you designed a large cell, would it be a large sphere or something long and flat?