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1. An aluminium sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The difference in the surface areas of the two solids would be :

A. Nil

B. 284 cm²

C. 286 cm²

D. 296 cm²

Solution:

Volume of cube = Volume of sheet = (27 × 8 × 1) cm³ = 216 cm³
Edge of cube :

\sqrt[3]{216} c m = 6 c m

Surface area of sheet :

\begin{aligned} = 2 (l b + b h + l h) \\ = 2 (27 \times 8 + 8 \times 1 + 27 \times 1) c m^{2} \\ = (216 + 8 + 27) c m^{2} \\ = 502 c m^{2} \end{aligned}

Surface area of cube :

\begin{aligned} = 6 a^{2} \\ = (6 \times 6^{2}) c m^{2} \\ = 216 c m^{2} \end{aligned}

∴ Required difference :

\begin{aligned} = (502 - 216) c m^{2} \\ = 286 c m^{2} \end{aligned}

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