Question

How many wooden cubical blocks of side 25 cm can be cut from a log of wood of size 3 m by 75 cm by 50 cm, assuming that there is no wastage?

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{dimension}\mathrm{of}\mathrm{the}\log \mathrm{of}\mathrm{wood}\mathrm{is}3\mathrm{m}\times 75\mathrm{cm}\times 50\mathrm{cm},\mathrm{i}.\mathrm{e}.,300\mathrm{cm}\times 75\mathrm{cm}\times 50\mathrm{cm}(\because 3\mathrm{m}=100\mathrm{cm}). \\ \therefore \mathrm{Volume}=300\mathrm{cm}\times 75\mathrm{cm}\times 50\mathrm{cm}=1125000{\mathrm{cm}}^3 \\ \mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{the}\mathrm{side}\mathrm{of}\mathrm{each}\mathrm{cubical}\mathrm{block}\mathrm{of}\mathrm{wood}\mathrm{is}\mathrm{of}25\mathrm{cm}. \\ \mathrm{Now},\mathrm{volume}\mathrm{of}\mathrm{one}\mathrm{cubical}\mathrm{block}=(\mathrm{side}{)}^3 \\ ={25}^3 \\ =15625{\mathrm{cm}}^3 \\ \therefore \mathrm{The}\mathrm{required}\mathrm{number}\mathrm{of}\mathrm{cubical}\mathrm{blocks}=\frac{\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{wood}\log }{\mathrm{volume}\mathrm{of}\mathrm{one}\mathrm{cubical}\mathrm{block}} \\ =\frac{1125000{\mathrm{cm}}^3}{15625{\mathrm{cm}}^3} \\ =72 \end{gathered}$$