The total surface area (in m²) of a cube, each of whose edges measures 192 m, is:

Appeared in: DSSSB 13 August 2024

Explanation

The total surface area (TSA) of a cube is calculated using the formula 6 × a², where 'a' represents the length of one edge.
A cube consists of six identical square faces. The area of a single face is a².
Given that the edge length 'a' is 192 m, the area of one face is 192 × 192 = 36,864 m².
Multiplying the area of one face by the total number of faces (6) gives the total surface area: 6 × 36,864 m² = 221,184 m².

Option B: This is a result of a calculation error and does not match the correct product of 6 × (192)², which is 221,184.
Option C: This is a result of a calculation error and does not match the correct product of 6 × (192)², which is 221,184.
Option D: This is a result of a calculation error and does not match the correct product of 6 × (192)², which is 221,184.

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 as background academic context rather than a clinical decision trigger.
Although a non-clinical question, it highlights the need for mathematical accuracy, a fundamental skill in nursing.
Nurses perform critical calculations for medication dosages, IV drip rates, and Body Surface Area (BSA), where precision is vital for patient safety.
What if the question asked for the volume of the cube? The formula would change to V = a³, and the calculation would be 192 × 192 × 192, resulting in a different answer and demonstrating the importance of using the correct formula for the required measurement.

How to Approach the Question

First, identify the key information provided in the question: the shape is a 'cube' and its 'edge measures 192 m'.
Next, determine what needs to be calculated: the 'total surface area'.
Recall the correct formula for the total surface area of a cube, which is TSA = 6 × a², where 'a' is the edge length.
Substitute the given value of 'a' (192 m) into the formula: TSA = 6 × (192)².
Execute the calculation in the correct order of operations (exponents first): 192² = 36,864. Then, multiply by 6: 6 × 36,864 = 221,184.
Finally, match your result (221,184) with the provided options to select the correct answer.

Concept Tested & Keywords

Q7f9NUJEbf-VGbSor1Ix53

Practise the full DSSSB 13 August 2024

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