Question

Find the number of cuboidal boxes measuring 2 cm by 3 cm by 10 cm which can be stored in a carton whose dimensions are 40 cm, 36 cm and 24 cm.

Answer 1

$$\begin{gathered} \mathrm{Dimension}\mathrm{of}\mathrm{one}\mathrm{cuboidal}\mathrm{box}=2\mathrm{cm}\times 3\mathrm{cm}\times 10\mathrm{cm} \\ \mathrm{Volume}=(2\times 3\times 10){\mathrm{cm}}^3=60{\mathrm{cm}}^3 \\ \mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{the}\mathrm{dimension}\mathrm{of}\mathrm{a}\mathrm{carton}\mathrm{is}40\mathrm{cm}\times 36\mathrm{cm}\times 24\mathrm{cm},\mathrm{where}\mathrm{the}\mathrm{boxes}\mathrm{can}\mathrm{be}\mathrm{sto}\mathrm{red}. \\ \therefore \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{carton}=(40\times 36\times 24){\mathrm{cm}}^3=34560{\mathrm{cm}}^3 \\ \therefore \mathrm{The}\mathrm{required}\mathrm{number}\mathrm{of}\mathrm{cuboidal}\mathrm{boxes}\mathrm{that}\mathrm{can}\mathrm{be}\mathrm{stored}\mathrm{in}\mathrm{the}\mathrm{carton}=\frac{\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{carton}}{\mathrm{volume}\mathrm{of}\mathrm{one}\mathrm{cuboidal}\mathrm{box}}=\frac{34560{\mathrm{cm}}^3}{60{\mathrm{cm}}^3}=576 \end{gathered}$$