If the volume of cube is 117649 m³, then find the total surface area of cube in m².

Appeared in: RRB Nsg Superintendent -29 April 2025 (Shift-1st)

Explanation

The first step is to determine the side length of the cube from its given volume.
The formula for the volume of a cube is V = a³, where 'a' is the side length. Therefore, a = ∛V.
Given V = 117649 m³, the side length 'a' is ∛117649, which is 49 m.
The second step is to calculate the total surface area (TSA) using the side length.
The formula for the TSA of a cube is 6a², as a cube has six identical square faces.
Substituting a = 49 m, the TSA is 6 × (49)² = 6 × 2401 = 14406 m².

Option A: This value is incorrect and likely results from a calculation error, such as miscalculating the square of the side length or the final multiplication.
Option B: This is an incorrect value. It might arise from an error in finding the cube root of the volume or a mistake in the multiplication for the surface area.
Option C: This value is incorrect. It could be the result of a miscalculation at any stage, either in determining the side length or in computing the final surface area.

Visual 1: Diagram - A 3D representation of a cube, with one side labeled 'a', the volume labeled 'V = a³', and the total surface area labeled 'TSA = 6a²'. This helps visualize the geometric properties and formulas.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of the total surface area of a cube from its volume as background academic context rather than a clinical decision trigger.
What if? - If the stem changed one defining clue so that 14406 no longer matched, reassess the option whose mechanism, classification, or indication now fits the revised presentation.

How to Approach the Question

First, identify the given information: the volume of the cube is 117649 m³.
Next, identify what needs to be found: the total surface area of the cube.
Recall the formula for the volume of a cube: V = a³, where 'a' is the side length.
Use the given volume to calculate the side length 'a' by finding the cube root of the volume: a = ∛117649.
Recall the formula for the total surface area of a cube: TSA = 6a².
Substitute the calculated side length 'a' into the TSA formula and compute the final answer.

Concept Tested & Keywords

Concept Tested: Calculation of the total surface area of a cube from its volume.
Stem keywords: volume of cube, 117649 m³, total surface area
Lead-in keywords: find

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Practise the full RRB Nsg Superintendent -29 April 2025 (Shift-1st)

Attempt every question from this paper in a timed mock, then review the full solution for each one.