Final answer:
The question pertains to finding the volume of a shipping container using the standard formula V = l x w x d. For certain shapes, specific formulas like V = s³ for a cube and V = 4/3 (pi) (r)³ for a sphere are used. Dimensional analysis assures the dimensional consistency of volume formulas.
Step-by-step explanation:
The student is asking for the standard form polynomial that represents the volume of a shipping container. In geometry, the volume of a rectangular container can be calculated using the formula V = length × width × depth (l x w x d). If the dimensions of the shipping container are given, they can be substituted into this formula to find the volume. For example, if the dimensions are 13.44 dm by 5.920 dm by 2.54 dm, then the volume would be calculated as 13.44 × 5.920 × 2.54 which gives 202.09459... dm³, rounded to three significant figures, the volume would be approximately 202 dm³, or 202 liters.
If the volume of another shape such as a sphere or a cube is needed, different formulas are used. For a cube with side 's', the volume formula is V = s³, while for a sphere with radius 'r', the volume formula is V = 4/3 (pi) (r)³. Dimensional analysis helps ensure that formulas used are dimensionally consistent, meaning each term in the formula has the correct units for volume.
Regarding the inquiry about volume of a sphere, it is important to distinguish volume from surface area. The volume of a sphere is given by the formula V = 4/3 (pi) (r)³, not 4(pi)(r)³ which instead represents surface area. To check if you have the correct volume formula, you can look at the dimensions of each term in the formula to see if they result in cubic units, which represent volume, such as cubic meters (m³).