To find the surface area to volume ratio (SA:V) for each cell, we need to calculate the surface area and the volume for each cube-shaped cell.
Formulas for a Cube:
*
Surface Area (SA) = $6 \times (\text{side length})^2$
*
Volume (V) = $(\text{side length})^3$
*
Ratio (SA:V) = $\frac{\text{Surface Area}}{\text{Volume}}$
Let's calculate this for each of the three cells shown.
1. Small Cell (Side length = $1 \mu m$)
*
Step 1: Calculate Surface Area
$$SA = 6 \times (1)^2$$
$$SA = 6 \times 1 = 6 \mu m^2$$
*
Step 2: Calculate Volume
$$V = (1)^3$$
$$V = 1 \times 1 \times 1 = 1 \mu m^3$$
*
Step 3: Calculate Ratio
$$SA:V = \frac{6}{1} = 6$$
2. Medium Cell (Side length = $2 \mu m$)
*
Step 1: Calculate Surface Area
$$SA = 6 \times (2)^2$$
$$SA = 6 \times 4 = 24 \mu m^2$$
*
Step 2: Calculate Volume
$$V = (2)^3$$
$$V = 2 \times 2 \times 2 = 8 \mu m^3$$
*
Step 3: Calculate Ratio
$$SA:V = \frac{24}{8} = 3$$
3. Large Cell (Side length = $4 \mu m$)
*
Step 1: Calculate Surface Area
$$SA = 6 \times (4)^2$$
$$SA = 6 \times 16 = 96 \mu m^2$$
*
Step 2: Calculate Volume
$$V = (4)^3$$
$$V = 4 \times 4 \times 4 = 64 \mu m^3$$
*
Step 3: Calculate Ratio
$$SA:V = \frac{96}{64}$$
To simplify $\frac{96}{64}$, we can divide both numbers by 32:
$$96 \div 32 = 3$$
$$64 \div 32 = 2$$
So, the ratio is $\frac{3}{2}$ or
1.5.
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Summary of Results:
* Cell with side $1 \mu m$: SA:V ratio is
6
* Cell with side $2 \mu m$: SA:V ratio is
3
* Cell with side $4 \mu m$: SA:V ratio is
1.5
Final Answer:
The surface area to volume ratios are:
- For the $1 \mu m$ cell:
6
- For the $2 \mu m$ cell:
3
- For the $4 \mu m$ cell:
1.5
Parent Tip: Review the logic above to help your child master the concept of surface area to volume ratio worksheet.
