Question

A large cube is formed from the material obtained by melting three smaller cubes of sides 3 cm, 4 cm and 5 cm. What is the ratio of the total surface area of the smaller cubes to the large cube?

Accepted Answer

C. Volume of new cube $V = 3^3 + 4^3 + 5^3 = 27 + 64 + 125 = 216	ext{ cm}^3$. Side of the new cube $A = \sqrt[3]{216} = 6	ext{ cm}$. Total surface area of the three smaller cubes $= 6(3^2 + 4^2 + 5^2) = 6(9 + 16 + 25) = 6(50) = 300	ext{ cm}^2$. Total surface area of the large cube $= 6(6^2) = 216	ext{ cm}^2$. Ratio $= \frac{300}{216} = \frac{25}{18}$.

Melting Cubes into a Large Cube

Explanation

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