A box is in the shape of a cube. The length of its outer edge is 5 m. Find the cost of painting all the outer surfaces of the box at the rate of ₹25 per m².

1. A

   ₹810

2. B

   ₹570

3. C

   ₹620

4. D

   ₹3750

Appeared in: NHM UP Staff Nurse-2023 Shift-2nd

Explanation

• The question requires calculating the total cost to paint the outer surface of a cubical box.
• First, find the total surface area (TSA) of the cube using the formula TSA = 6 × a², where 'a' is the edge length.
• Given a = 5 m, the TSA = 6 × (5)² = 6 × 25 = 150 m².
• Next, calculate the total cost by multiplying the TSA by the painting rate.
• Total Cost = 150 m² × ₹25/m² = ₹3750.

Why Other Options Were Wrong

• Option A: This value is an incorrect calculation and does not logically follow from the problem's data.
• Option B: This is a miscalculation. It does not represent the surface area or a logical derivative of it multiplied by the cost.
• Option C: This value is incorrect. It may result from a calculation error.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Surface Area of a Cube as background academic context rather than a clinical decision trigger.
• This question tests foundational quantitative aptitude, specifically geometry and arithmetic, which is a component of many competitive examinations.
• The ability to perform multi-step calculations accurately is essential. A common error is to calculate the area of only one face (5 × 5 = 25 m²) and multiply by the cost, or to mistakenly calculate the volume (5³ = 125 m³) instead of the surface area.
• What if the question asked to paint only the four side walls and the top (an open box)? The area would be 5 × (a²) = 5 × 25 = 125 m², and the cost would be 125 × ₹25 = ₹3125.

How to Approach the Question

• First, identify the key information provided: the shape is a cube, the edge length is 5 m, and the painting cost is ₹25 per m².
• Recognize that 'painting all the outer surfaces' requires calculating the Total Surface Area (TSA) of the cube.
• Recall the formula for the TSA of a cube: TSA = 6 × (edge length)².
• Substitute the given edge length into the formula: TSA = 6 × (5)².
• Perform the calculation: TSA = 6 × 25 = 150 m².
• Finally, calculate the total cost by multiplying the TSA by the rate per square meter: Total Cost = 150 × 25 = ₹3750.

Concept Tested & Keywords

• Concept Tested: Surface Area of a Cube
• Stem keywords: cube, outer edge, cost of painting, surface area
• Lead-in keywords: Find the cost

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