Question

Divide the volume expression by its width (w-3).

a) (V / (w - 3))
b) (V / w) - 3
c) V / (w - 3)
d) V / w - 3

Answer 1

The correct way to divide a volume expression by its width (w - 3) is represented as V / (w - 3), which treats (w - 3) as one entity.

Step-by-step explanation:

When dividing the volume expression by its width, denoted as (w - 3), the correct mathematical representation is V / (w - 3). This indicates that you are dividing the entire volume V by the width expression (w - 3), treating w - 3 as a single entity. Misinterpreting the placement of parentheses can lead to different results; thus accuracy in notation is crucial in mathematics, especially in algebra.

The formula for the volume of a sphere, which is another common geometric problem, is 4πr3 / 3. The given information about volumes and the multiplicative factor of pi/3 seems to allude to finding a volume based on a modified form of the volume of a sphere. In dimensional analysis, it's vital to ensure that formulas are consistent and correct as seen in the exercise to discern dimensionally consistent formulas for volume and area.