Question

Three cubes of metal with edges 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. The lateral surface area of the new cube formed is
(a) 72 cm²
(b) 144 cm²
(c) 128 cm²
(d) 256 cm²

Answer 1

(b) 144 cm²
Volume of the new cube formed = total volume of the three cubes
Suppose that a cm is the edge of the new cube, then

$$\begin{gathered} a^3=3^3+4^3+5^3 \\ =27+64+125 \\ =216 \\ =6\mathrm{cm} \end{gathered}$$

∴ Lateral surface area of the new cube = $4a^2=4\times 6\times 6=144{\mathrm{cm}}^2$