ABC26GN4846 · Volume and Surface Area
Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2008 · Marks: · Difficulty:
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)$284 \mathrm{cm}^{2}$
(c)$286 \mathrm{cm}^{2}$
(d)$296 \mathrm{cm}^{2}$
Answer
Explanation
Volume of cube = Volume of sheet $=(27 \times 8 \times 1) \mathrm{cm}^{3}=$ $216 \mathrm{cm}^{3}$. Edge of cube $=\sqrt[3]{216} \mathrm{cm}=6 \mathrm{cm}$. Surface area of sheet $=2(l b+b h+l h)=2(27 \times 8+8 \times 1$ $$+27 \times 1) \mathrm{cm}^{2} \text {. } =(216+8+27) \mathrm{cm}^{2}=502 \mathrm{cm}^{2} .$$ Surface area of cube $=6 a^{2}=\left(6 \times 6^{2}\right) \mathrm{cm}^{2}=216 \mathrm{cm}^{2}$. ∴ Required difference $=(502-216) \mathrm{cm}^{2}=286 \mathrm{cm}^{2}$.
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