The curved surface area of a right circular cylinder of base radius R, in terms of volume V, is:

ESIC Nursing Officer - 2019 (Shift-2)

Non Nursing Subjects

Hard

Appeared in: ESIC Nursing Officer - 2019 (Shift-2)

Explanation

The volume (V) of a cylinder is V = π * R² * h, and the curved surface area (CSA) is CSA = 2 * π * R * h.
To express CSA in terms of V and R, first isolate height (h) from the volume formula: h = V / (π * R²).
Substitute this expression for h into the CSA formula: CSA = 2 * π * R * [V / (π * R²)].
Simplifying the expression by canceling π and one R term gives CSA = 2V / R.

Option A: This option incorrectly multiplies V and R. The derivation shows that R should be in the denominator.
Option B: This option is missing the factor of 2. The formula for CSA includes a '2' (from 2 * π * R * h), which remains after simplification.
Option C: This option incorrectly multiplies V by R instead of dividing. This would imply that as the radius increases (for a fixed volume), the surface area also increases, which is incorrect.

Visual 1: Diagram - An annotated diagram of a right circular cylinder, clearly labeling the radius (R), height (h), base area, and curved surface area. This helps visualize the components used in the formulas.
Visual 2: Infographic - A flowchart showing the step-by-step derivation: Start with V and CSA formulas -> Isolate h from V formula -> Substitute h into CSA formula -> Simplify to get the final expression. This reinforces the logical process.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Relationship between Volume and Surface Area of a Cylinder as background academic context rather than a clinical decision trigger.
While this is a mathematics question, understanding geometric relationships is foundational for many scientific and medical calculations, such as calculating the volume of a vial or the surface area of a cylindrical cast.
This skill in algebraic manipulation is crucial for dosage calculations where formulas must be rearranged to solve for an unknown variable.
What if the question asked for the Total Surface Area (TSA) in terms of V and R? The process would be similar: TSA = 2 * π * R * (h + R) = 2 * π * R * h + 2 * π * R². Substituting h = V / (π * R²) gives TSA = 2V/R + 2 * π * R², demonstrating how different properties are related.

How to Approach the Question

Identify the key geometric shape: a right circular cylinder.
List the standard formulas associated with this shape: Volume (V = π * R² * h) and Curved Surface Area (CSA = 2 * π * R * h).
Analyze the goal: Express CSA using only the variables V and R. This means the variable 'h' must be eliminated.
Use algebraic substitution. Rearrange the volume formula to solve for the variable you want to eliminate (h).
Substitute the resulting expression for 'h' into the CSA formula.
Simplify the final algebraic expression to match one of the given options.

Concept Tested & Keywords

Concept Tested: Relationship between Volume and Surface Area of a Cylinder
Stem keywords: Curved surface area, right circular cylinder, base radius R, volume V
Lead-in keywords: BEST, MOST RELEVANT CLUE

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