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 $\boxed{{\displaystyle 1}}{\text{ unit}}^{-1}$.