Question

The weight of a metal block of size 5 cm by 4 cm by 3 cm is 1 kg. Find the weight of a block of the same metal of size 15 cm by 8 cm by 3 cm.

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{weight}\mathrm{of}\mathrm{the}\mathrm{metal}\mathrm{block}\mathrm{of}\mathrm{dimension}5\mathrm{cm}\times 4\mathrm{cm}\times 3\mathrm{cm}\mathrm{is}1\mathrm{kg}. \\ \mathrm{Its}\mathrm{volume}=\mathrm{length}\times \mathrm{breadth}\times \mathrm{height}=(5\times 4\times 3){\mathrm{cm}}^3=60{\mathrm{cm}}^3 \\ \mathrm{i}.\mathrm{e}.,\mathrm{the}\mathrm{weight}\mathrm{of}60{\mathrm{cm}}^3\mathrm{of}\mathrm{the}\mathrm{metal}\mathrm{is}1\mathrm{kg} \\ \mathrm{Again},\mathrm{the}\mathrm{dimension}\mathrm{of}\mathrm{the}\mathrm{other}\mathrm{block}\mathrm{which}\mathrm{is}\mathrm{of}\mathrm{same}\mathrm{metal}\mathrm{is}15\mathrm{cm}\times 8\mathrm{cm}\times 3\mathrm{cm}. \\ \mathrm{Its}\mathrm{volume}=\mathrm{length}\times \mathrm{breadth}\times \mathrm{height}=(15\times 8\times 3){\mathrm{cm}}^3=360{\mathrm{cm}}^3 \\ \therefore \mathrm{The}\mathrm{weight}\mathrm{of}\mathrm{the}\mathrm{required}\mathrm{block}=360{\mathrm{cm}}^3 \\ =6\times 60{\mathrm{cm}}^3(\because \mathrm{Weight}\mathrm{of}60{\mathrm{cm}}^3\mathrm{of}\mathrm{the}\mathrm{metal}\mathrm{is}1\mathrm{Kg}) \\ =6\times 1\mathrm{kg} \\ =6\mathrm{kg} \end{gathered}$$