Question

The dimensions of a metal block are 2.25 m by 1.5 m by 27 cm. It is melted and recast into cubes, each of the side 45 cm. How many cubes are formed?

Answer 1

$$\begin{gathered} \mathrm{Dimension}\mathrm{of}\mathrm{the}\mathrm{metal}\mathrm{block}\mathrm{is}2.25\mathrm{m}\times 1.5\mathrm{m}\times 27\mathrm{cm},\mathrm{i}.\mathrm{e}.,225\mathrm{cm}\times 150\mathrm{cm}\times 27\mathrm{cm}(\because 1\mathrm{m}=100\mathrm{cm}). \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{metal}\mathrm{block}=225\times 150\times 27=911250{\mathrm{cm}}^3 \\ \mathrm{This}\mathrm{metal}\mathrm{block}\mathrm{is}\mathrm{melted}\mathrm{and}\mathrm{recast}\mathrm{into}\mathrm{cubes}\mathrm{each}\mathrm{of}\mathrm{side}45\mathrm{cm}. \\ \mathrm{Volume}\mathrm{of}\mathrm{a}\mathrm{cube}=(\mathrm{side}{)}^3={45}^3=91125{\mathrm{cm}}^3 \\ \therefore \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{such}\mathrm{cubes}\mathrm{formed}\mathrm{from}\mathrm{the}\mathrm{metal}\mathrm{block}=\frac{\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{metal}\mathrm{block}}{\mathrm{volume}\mathrm{of}a\mathrm{metal}\mathrm{cube}}=\frac{911250{\mathrm{cm}}^3}{91125{\mathrm{cm}}^3}=10 \end{gathered}$$