A large cube is formed by melting three smaller solid cubes of edges 3 cm, 4 cm, and 5 cm. What is the ratio of the total surface area of the three small cubes to that of the large cube?

Problem Restatement

Use volume conservation to get the large cube's edge, then compare total surface areas.

Given data

• Small cube edges: 3 cm, 4 cm, 5 cm

Step 1: Find large cube edge

Total volume = 3^3 + 4^3 + 5^3 = 27 + 64 + 125 = 216 cm^3Large cube edge a satisfies a^3 = 216 → a = 6 cm

Step 2: Compare total surface areas

TSA (three small) = 6(3^2 + 4^2 + 5^2) = 6(9 + 16 + 25) = 6 × 50 = 300 cm^2TSA (large) = 6a^2 = 6 × 36 = 216 cm^2Required ratio = 300 : 216 = 25 : 18

Final Answer

Ratio of areas = 25 : 18.