The cost of paint is Rs. 36.50 per kg. If 1 kg of paint covers 16 square feet, how much will it cost to paint the outside surface of a solid cube having each edge 8 feet long?

Introduction / Context:
This is a practical mensuration problem involving the surface area of a cube and a unit rate for painting. It appears often in aptitude tests that combine geometry with cost calculations. The key steps are to find the total area to be painted, determine how many kilograms of paint are needed, and then multiply by the given cost per kilogram.

Given Data / Assumptions:
• The solid is a cube.• Edge length of the cube = 8 feet.• Cost of paint = Rs. 36.50 per kg.• Coverage of paint = 1 kg covers 16 square feet.• Entire external surface area of the cube is to be painted once.

Concept / Approach:
The surface area of a cube with side a is given by 6a^2, because it has six identical square faces. Once we compute the total area, we divide by the coverage per kilogram to find the quantity of paint required. Finally, we multiply the number of kilograms by the cost per kilogram. If the result is a whole number of kilograms, the cost will be a simple multiplication; otherwise, we might need to consider fractions, but in this case the numbers work out neatly.

Step-by-Step Solution:
Step 1: Compute total surface area of the cube.Side a = 8 ft.Surface area = 6 * a^2 = 6 * 8^2.8^2 = 64, so area = 6 * 64 = 384 square feet.Step 2: Compute how many kilograms of paint are required.1 kg covers 16 sq. ft., so paint required = total area / coverage per kg.Paint required = 384 / 16 = 24 kg.Step 3: Compute the cost.Cost per kg = Rs. 36.50.Total cost = 24 * 36.50.24 * 36.50 = 876.So total cost = Rs. 876.

Verification / Alternative check:
We can check the multiplication by breaking 36.50 into 36 and 0.50. Then 24 * 36 = 864 and 24 * 0.50 = 12. Adding them gives 864 + 12 = 876, which matches the earlier product. The paint requirement of 24 kg also makes sense because 384 sq. ft. divided by 16 sq. ft. per kg is exactly 24, with no remainder, confirming the coverage calculation.

Why Other Options Are Wrong:
Option A: Rs.962 comes from an incorrect multiplication or a different assumed coverage.Option B: Rs.672 is too low and ignores part of the surface area or uses a wrong cost per kilogram.Option C: Rs.546 also does not match the correct product of 24 and 36.50.

Common Pitfalls:
Students sometimes forget that a cube has six faces and mistakenly use 4a^2 or 2a^2 instead of 6a^2. Others may divide the total area by the cost per kilogram rather than the coverage, or mix up units. Double checking which numbers represent area, coverage, and cost helps prevent these mistakes, as does rewriting the steps clearly before calculating.

Final Answer:
The cost of painting the outside of the cube is Rs.876.