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

1 answer

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}