Question

How many soap cakes can be placed in a box of size 56 cm × 0.4 m × 0.25 m, if the size of a soap cake is 7 cm × 5 cm × 2.5 cm?

Answer 1

$$\begin{gathered} \mathrm{Dimension}\mathrm{of}\mathrm{a}\mathrm{soap}\mathrm{cake}=7\mathrm{cm}\times 5\mathrm{cm}\times 2.5\mathrm{cm} \\ \mathrm{Its}\mathrm{volum}e=\mathrm{length}\times \mathrm{breadth}\times \mathrm{height}=(7\times 5\times 2.5){\mathrm{cm}}^3=87.5{\mathrm{cm}}^3 \\ \mathrm{Also},\mathrm{the}\mathrm{dimension}\mathrm{of}\mathrm{the}\mathrm{box}\mathrm{that}\mathrm{contains}\mathrm{the}\mathrm{soap}\mathrm{cakes}\mathrm{is}56\mathrm{cm}\times 0.4\mathrm{m}\times 0.25\mathrm{m},\mathrm{i}.\mathrm{e}.,56\mathrm{cm}\times 40\mathrm{cm}\times 25\mathrm{cm}(\because 1\mathrm{m}=100\mathrm{cm}). \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{box}=\mathrm{length}\times \mathrm{breadth}\times \mathrm{height}=(56\times 40\times 25){\mathrm{cm}}^3=56000{\mathrm{cm}}^3 \\ \therefore \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{soap}\mathrm{cakes}\mathrm{that}\mathrm{can}\mathrm{be}\mathrm{placed}\mathrm{inside}\mathrm{the}\mathrm{box}=\frac{\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{box}}{\mathrm{volume}\mathrm{of}\mathrm{a}\mathrm{soap}\mathrm{cake}}=\frac{56000{\mathrm{cm}}^3}{87.5{\mathrm{cm}}^3}=640 \end{gathered}$$