Question

Suppose you discovered a new multicellular organism that is shaped like a cube. The organism measures 3 cells tall, 3 cells wide, and 3 cells deep. You measure one cubed cell to be 2 arbitrary units per side. Can you calculate this organism’s surface area to volume ratio?

Find the surface area, volume, and surface area to volume ratio

Answer 1

To find the surface area, volume, and surface area to volume ratio of the new cubical organism, we can follow these steps:

### Step 1: Determine the dimensions of the organism
The organism has dimensions of 3 cells tall, 3 cells wide, and 3 cells deep. Given that each cubed cell measures 2 arbitrary units per side, we can calculate the overall dimensions of the organism in arbitrary units.

- Height = 3 cells × 2 units/cell = 6 units
- Width = 3 cells × 2 units/cell = 6 units
- Depth = 3 cells × 2 units/cell = 6 units

### Step 2: Calculate the volume
The volume \( V \) of a cuboid is given by the formula:
\[
V = \text{Height} \times \text{Width} \times \text{Depth}
\]

Substituting the dimensions we found:
\[
V = 6 \, \text{units} \times 6 \, \text{units} \times 6 \, \text{units} = 216 \, \text{cubic units}
\]

### Step 3: Calculate the surface area
The surface area \( A \) of a cuboid is given by the formula:
\[
A = 2(\text{Height} \times \text{Width} + \text{Height} \times \text{Depth} + \text{Width} \times \text{Depth})
\]

Substituting the dimensions:
\[
A = 2(6 \, \text{units} \times 6 \, \text{units} + 6 \, \text{units} \times 6 \, \text{units} + 6 \, \text{units} \times 6 \, \text{units})
\]
\[
A = 2(36 + 36 + 36) = 2(108) = 216 \, \text{square units}
\]

### Step 4: Calculate the surface area to volume ratio
The surface area to volume ratio \( R \) is given by:
\[
R = \frac{A}{V}
\]

Substituting the values we calculated:
\[
R = \frac{216 \, \text{square units}}{216 \, \text{cubic units}} = 1 \, \text{(arbitrary units)}^{-1}
\]

### Summary of Results
- **Surface Area**: 216 square units
- **Volume**: 216 cubic units
- **Surface Area to Volume Ratio**: 1 (arbitrary units)^{-1}