Final answer:
Dimensional analysis involves checking that units in formulas are appropriate for their quantity. Formulas a, b, and e are dimensionally consistent, representing volumes and areas with proper units like m³ (for volume) and m² (for areas), while c and d are not consistent for the volumes they claim to represent.
Step-by-step explanation:
When assessing the formulas for dimensional consistency in the context of geometry, it's crucial to ensure that the units correctly represent the quantity being measured, whether it's area, volume, or length. Let's look at each formula:
- Formula a: V = ² = πr² h is dimensionally consistent because it represents volume (V), which should have a unit of length cubed (e.g., m³). This formula is for the volume of a cylinder, where r is the radius and h is the height.
- Formula b: A = 2λr² + 2λrh is dimensionally consistent for area (A), as it accounts for the two areas of the circle (2λr², the circles on the top and bottom) and the area of the rectangle that wraps around the cylinder (2λrh).
- Formula c: V = 0.5bh is not dimensionally consistent for volume since the formula 0.5bh typically represents the area of a triangle, not volume.
- Formula d: V = ñd² is not dimensionally consistent since d² represents an area, and for volume, we would expect a term with length cubed.
- Formula e: V = λd³ 16 is dimensionally consistent for volume as d³ represents cubic units, which is correct for volume.