Discussion
A metallic solid cuboidal box of dimensions \(200\text{ cm} \times 50\text{ cm} \times 100\text{ cm}\) is melted and recast into a solid cube. The difference between the surface areas of the two solids is
Answer: D
The difference is 10000 cm2.
The volume stays the same when the box is recast:
\[ \begin{aligned} V &= 200 \times 50 \times 100 = 10^{6}\ \text{cm}^{3} \\ \text{side} &= \sqrt[3]{10^{6}} = 100\ \text{cm} \\ S_{\text{cuboid}} &= 2(10000 + 5000 + 20000) \\ &= 70000 \\ S_{\text{cube}} &= 6 \times 100^{2} = 60000 \end{aligned} \]
The difference is 70000 - 60000 = 10000 cm2. The cube has the smaller surface area, as expected: for a fixed volume, a cube encloses it with less surface than an elongated box.
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