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?

Answer 1

To calculate the surface area to volume ratio for the cubic organism, we first need to determine the surface area and volume.

1. Finding the dimensions: Each cell measures 2 arbitrary units per side. Since the organism is 3 cells tall, 3 cells wide, and 3 cells deep, the total dimensions of the organism in arbitrary units are: \[ \text{Height} = 3 \text{ cells} \times 2 \text{ units/cell} = 6 \text{ units} \] \[ \text{Width} = 3 \text{ cells} \times 2 \text{ units/cell} = 6 \text{ units} \] \[ \text{Depth} = 3 \text{ cells} \times 2 \text{ units/cell} = 6 \text{ units} \]

2. Calculating the volume (V): The volume of a rectangular prism is given by the formula: \[ V = \text{Height} \times \text{Width} \times \text{Depth} \] Substituting in our dimensions: \[ V = 6 \text{ units} \times 6 \text{ units} \times 6 \text{ units} = 216 \text{ cubic units} \]

3. Calculating the surface area (SA): The surface area of a rectangular prism can be calculated using the formula: \[ SA = 2 \times (\text{Height} \times \text{Width} + \text{Height} \times \text{Depth} + \text{Width} \times \text{Depth}) \] Substituting in our dimensions: \[ SA = 2 \times (6 \times 6 + 6 \times 6 + 6 \times 6) \] \[ = 2 \times (36 + 36 + 36) = 2 \times 108 = 216 \text{ square units} \]

4. Calculating the surface area to volume ratio (SA/V): The surface area to volume ratio is given by: \[ \text{Ratio} = \frac{SA}{V} = \frac{216 \text{ square units}}{216 \text{ cubic units}} = 1 \text{ unit}^{-1} \]

Therefore, the surface area to volume ratio of this cubic organism is \( \boxed{1} \text{ unit}^{-1} \).