The internal surface area (in m²) of an open cuboidal tank whose internal length, internal breadth, and internal height are given as 31 m, 20 m, and 22 m, respectively, is:

1. A

   2864

2. B

   2900

3. C

   2827

4. D

   2899

Appeared in: DSSSB 14 August 2024

Explanation

• The question asks for the internal surface area of an 'open' cuboidal tank, which means it has a base and four walls, but no top.
• The correct formula for this is the area of the base (length × breadth) plus the lateral surface area (2 × height × (length + breadth)).
• Given: l = 31 m, b = 20 m, h = 22 m.
• Area of base = 31 × 20 = 620 m².
• Lateral surface area = 2 × 22 × (31 + 20) = 44 × 51 = 2244 m².
• Total surface area = 620 + 2244 = 2864 m².

Why Other Options Were Wrong

• Option B: This value is incorrect. It may result from a miscalculation, such as incorrectly summing the area of the base and the lateral surface area.
• Option C: This value is incorrect. It is likely the result of an arithmetic error during the multiplication or addition steps of the calculation.
• Option D: This value is incorrect and close to the correct answer, suggesting a minor calculation error could lead to this choice.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of the surface area of an open cuboid as background academic context rather than a clinical decision trigger.
• While not a direct clinical skill, this type of question tests general aptitude and mathematical reasoning, which are often included in nursing entrance and recruitment examinations.
• Strong analytical and calculation skills are foundational for tasks like medication dosage calculation, fluid balance monitoring, and interpreting quantitative data in patient care.
• What if the tank was closed? If the tank were closed, you would need to calculate the total surface area using the formula 2(lb + bh + hl). The area would be 2 × (620 + 440 + 682) = 2 × 1742 = 3484 m².

How to Approach the Question

• First, identify the shape described in the question, which is a 'cuboidal tank'.
• Next, note the specific condition mentioned: the tank is 'open'. This is a critical detail as it means you should not include the area of the top surface.
• Recall or write down the correct formula for the surface area of an open cuboid: Area = (Area of Base) + (Area of 4 Walls) = (l × b) + 2h(l + b).
• Substitute the given values for length (l=31), breadth (b=20), and height (h=22) into the formula.
• Perform the calculation in steps to avoid errors: first calculate the base area, then the lateral area, and finally add them together.
• Compare your final calculated result with the given options to find the correct answer.

Concept Tested & Keywords

• Concept Tested: Calculation of the surface area of an open cuboid.
• Stem keywords: internal surface area, open cuboidal tank, length, breadth, height
• Lead-in keywords: is:

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QKpIJTZtWjUStOunBZ632d

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