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

### Concept & Logic To find the cost of painting the outside of a cube, we first need to determine the total surface area to be painted. Then, find out how many kilograms of paint are required by dividing the area by the coverage per kg. Finally, multiply the required kg by the cost per kg. $$Surface Area = 6a^2$$ $$Total Cost = \left(\frac{Surface Area}{Coverage per kg}\right) \times Cost per kg$$ ### Step-by-Step Solution 1. **Calculate Surface Area:** Side $a = 8$ feet. $Surface Area = 6 \times 8^2 = 6 \times 64 = 384$ square feet. 2. **Calculate Paint Required:** 1 kg covers 16 sq. feet. Paint required $= \frac{384}{16} = 24$ kg. 3. **Calculate Total Cost:** Cost per kg $= 36.50$. Total Cost $= 24 \times 36.50$ Total Cost $= 24 \times (36 + 0.50) = 864 + 12 = 876$. ### Exam Strategy & Shortcut Break down the multiplication for faster mental math: $24 \times 36.5 = 24 \times \frac{73}{2} = 12 \times 73$. $12 \times 70 = 840$ and $12 \times 3 = 36$. $840 + 36 = 876$. ### Common Pitfall Calculating the volume ($8^3 = 512$) instead of the surface area ($6 \times 8^2 = 384$). Painting always relates to surface area, not volume. ### Final Answer Therefore, the correct answer is **₹ 876**.