Question

a cube with slides 4 cm long is painted on all faces. It is then cut into cubes with sides I cm long. How many of these small cubes we have: 2

a) 3,2,1and no surface painted

Answer 1

$$\begin{gathered} \mathrm{Dear}\mathrm{Student}, \\ \mathrm{Cube}\mathrm{is}\mathrm{cut}\mathrm{into}\mathrm{the}\mathrm{cubes}\mathrm{of}1\mathrm{cm}\mathrm{long}\mathrm{so}\mathrm{there}\mathrm{are}\mathrm{total}\mathrm{cubes} \\ =4\times 4\times 4=64\mathrm{cubes}. \\ \mathrm{Now}\mathrm{the}\mathrm{cubes}\mathrm{which}\mathrm{will}\mathrm{be}\mathrm{on}\mathrm{corners}\mathrm{have}\mathrm{three}\mathrm{side}\mathrm{painted} \\ \mathrm{So}\mathrm{number}\mathrm{of}\mathrm{three}\mathrm{side}\mathrm{painted}\mathrm{cubes}=8 \\ \mathrm{Now}\mathrm{number}\mathrm{of}\mathrm{cubes}\mathrm{with}\mathrm{two}\mathrm{face}\mathrm{painted}\mathrm{are}\mathrm{the}\mathrm{cubes}\mathrm{on}\mathrm{the}\mathrm{edges} \\ \mathrm{excluding}\mathrm{cubes}\mathrm{on}\mathrm{corners} \\ =3\times 6=18\mathrm{cubes} \\ \mathrm{Now}\mathrm{number}\mathrm{of}\mathrm{cubes}\mathrm{with}\mathrm{one}\mathrm{face}\mathrm{painted} \\ =\mathrm{outer}\mathrm{cubes}-\mathrm{three}\mathrm{face}\mathrm{painted}\mathrm{cubes}-\mathrm{two}\mathrm{face}\mathrm{painted}\mathrm{cubes} \\ =2\times 2\times 6 \\ =24 \\ \mathrm{Now}\mathrm{cubes}\mathrm{with}\mathrm{no}\mathrm{face}\mathrm{painted}=64-24-8-18=40-26=14 \\ \mathrm{Regards} \end{gathered}$$