Question

How many planks each of which is 3 m long, 15 cm broad and 5 cm thick can be prepared from a wooden block 6 m long, 75 cm broad and 45 cm thick?

Answer 1

$$\begin{gathered} \mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{wooden}\mathrm{block}=6\mathrm{m} \\ =6\times 100\mathrm{cm}(\because 1\mathrm{m}=100\mathrm{cm}) \\ =600\mathrm{cm} \\ \mathrm{Breadth}\mathrm{of}\mathrm{the}\mathrm{block}=75\mathrm{cm} \\ \mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{block}=45\mathrm{cm} \\ \mathrm{Volume}\mathrm{of}\mathrm{block}=\mathrm{length}\times \mathrm{breadth}\times \mathrm{height} \\ =600\times 75\times 45 \\ =2025000{\mathrm{cm}}^3 \\ \mathrm{Again},\mathrm{it}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{a}\mathrm{plank}=3\mathrm{m} \\ =3\times 100\mathrm{cm}(\because 1\mathrm{m}=100\mathrm{cm}) \\ =300\mathrm{cm} \\ \mathrm{Breadth}=15\mathrm{cm}, \\ \mathrm{Height}=5\mathrm{cm} \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{plank}=\mathrm{leng}\mathrm{th}\times \mathrm{breadth}\times \mathrm{height} \\ =300\times 15\times 5=22500{\mathrm{cm}}^3 \\ \therefore \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{such}\mathrm{planks}=\frac{\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{wooden}\mathrm{block}}{\mathrm{voume}\mathrm{of}\mathrm{a}\mathrm{plank}}=\frac{2025000{\mathrm{cm}}^3}{22500{\mathrm{cm}}^3}=90 \end{gathered}$$