If the volume of a cube is 27,000m3then find the total surface area of the cube in $\mathrm{m}^2

Appeared in: RRB Nsg. Superintendent-2026 (Shift -3rd)

Explanation

The volume of a cube is given by the formula V = a³, where 'a' is the side length.
Given the volume is 27,000 m³, the side length 'a' is the cube root of 27,000, which is 30 m.
The total surface area (TSA) of a cube is calculated using the formula TSA = 6a².
Substituting the side length, TSA = 6 × (30)² = 6 × 900 = 5400 m².

Option A: This value is incorrect and does not correspond to the correct calculation. It may result from a miscalculation of the side length or an error in applying the surface area formula.
Option C: This is an incorrect numerical value. It does not follow from the application of the standard formulas for a cube's volume and surface area.
Option D: This value is incorrect. It might be the result of a simple arithmetic error during the multiplication step (e.g., 6 × 900 + 3).

Visual 1: Diagram - A 3D diagram of a cube with one side labeled as 'a = 30 m', illustrating the dimensions used in the calculation.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Geometry: Calculating the surface area of a cube from its volume as background academic context rather than a clinical decision trigger.
This question tests fundamental mathematical and problem-solving skills, which are essential for nurses in various aspects of their practice.
Nurses use similar calculations for tasks like determining medication dosages, calculating IV drip rates, and interpreting patient data charts, all of which require accuracy and attention to detail.
What if the question asked for the lateral surface area? The formula would be 4a², resulting in 4 × (30)² = 3600 m², as it excludes the top and bottom faces.

How to Approach the Question

Step 1: Identify the given information, which is the volume of the cube (27,000 m³).
Step 2: Recall the formula for the volume of a cube: Volume = a³, where 'a' is the side length.
Step 3: Use the given volume to solve for the side length 'a'. Calculate the cube root of 27,000.
Step 4: Once the side length 'a' is found, recall the formula for the total surface area of a cube: TSA = 6a².
Step 5: Substitute the value of 'a' into the TSA formula and perform the calculation to find the final answer.
Step 6: Compare the calculated result with the given options to select the correct one.

Concept Tested & Keywords

Concept Tested: Geometry: Calculating the surface area of a cube from its volume.
Stem keywords: volume of a cube, total surface area, cube
Lead-in keywords: find
Negative lead-in flag: false

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