A cube whose volume is 1 / 8 cubic centimetre is placed on top of a cube whose volume is 1 cm3. The two cubes are then placed on top of a third cube whose volume is 8 cm3. The height of stacked cubes is

Let the volume of the three cubes be V1, V2 and V3 and a1, a2 and a3 be the sides of the cube.
\(\Rightarrow \mathrm{a}^{3}=\mathrm{V}\\ \Rightarrow \mathrm{a}_{1}^{3}=\mathrm{V}_{1} \\ \Rightarrow \mathrm{a}_{1}^{3}=\frac{1}{8} \\ \Rightarrow \mathrm{a}_{1}=\frac{1}{2} \mathrm{~cm}\\ Similarly,\\ \Rightarrow \mathrm{a}_{2}^{3}=1 \\ \Rightarrow \mathrm{a}_{2}=1 \mathrm{~cm}\\ \Rightarrow \mathrm{a}_{3}^{3}=8 \Rightarrow \mathrm{a}_{3}=2 \mathrm{~cm} \\ \text { The height of the resulting structure } =\frac{1}{2}+1+2 \\ =0.5+1+2 \\ =3.5 \mathrm{~cm}\)

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