# 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.
$$\Rightarrow \mathrm{a}^{3}=\mathrm{V}\\ \Rightarrow \mathrm{a}_{1}^{3}=\mathrm{V}_{1} \\ \Rightarrow \mathrm{a}_{1}^{3}=\frac{1}{8} \\ \Rightarrow \mathrm{a}_{1}=\frac{1}{2} \mathrm{~cm}\\ Similarly,\\ \Rightarrow \mathrm{a}_{2}^{3}=1 \\ \Rightarrow \mathrm{a}_{2}=1 \mathrm{~cm}\\ \Rightarrow \mathrm{a}_{3}^{3}=8 \Rightarrow \mathrm{a}_{3}=2 \mathrm{~cm} \\ \text { The height of the resulting structure } =\frac{1}{2}+1+2 \\ =0.5+1+2 \\ =3.5 \mathrm{~cm}$$