Question

A cube of side 8 cm is painted red, blue and yellow on opposite faces and is then cut into cubes of 1 cm side each. How many cubes have colour on at least one face?

Answer 1

$$\begin{gathered} \text{Given, side of cube=8 cm} \\ \text{So, Total no. of cubes=}{\left(\text{side}\right)}^3={\left(8\right)}^3=512 \\ \text{The no. of cubes having no face colour=}{\left(8-2\right)}^3=6^3=216 \\ \text{Thus,} \\ \text{No. of cubes having atleast one face coloured=Total no. of cubes-No. of cubes having no face coloured} \\ =512-216 \\ =\mathbf{296} \end{gathered}$$