Given a right cylinder where h is the height and r is the radius, what does the expression 2rh represent?A.Lateral areaB.VolumeC.AreaD.Base area

Break Down the Problem

1. Identify the characteristics of a right cylinder.
2. Understand the significance of height (h) and radius (r).
3. Analyze what the expression $2rh$ could represent in the context of a cylinder.

Relevant Concepts

1. Lateral Area of a Cylinder: The lateral area (or curved surface area) of a right cylinder is calculated using the formula: $Lateral\ Area = 2\pi rh$
2. Volume of a Cylinder: The volume is given by: $Volume = \pi r^2 h$
3. Base Area of a Cylinder: The area of the base (circle) is calculated as: $Base\ Area = \pi r^2$

Analysis and Detail

1. The lateral area is specifically designed to encapsulate the surface surrounding the cylinder, excluding the top and bottom.
2. The expression $2rh$ does not incorporate $\pi$, which is essential for circular measurements. Thus, it cannot represent the volume or base area.

Verify and Summarize

The expression $2rh$ resembles a part of the formula for lateral area but lacks the $\pi$ factor. Thus, it accurately corresponds to a portion of the lateral area calculation, specifically when considering the dimensions without the circular factor.

Final Answer

The expression $2rh$ represents A. Lateral area.