the cross section of a piece of metal 4m in length is indicated in figure below, find : (i) area of cross section (ii) the volume of piece of metal in cubic cms, if 1 cubic cm of metal weighs 6.6 g, calculate the weight of piece of metal to nearest kg.

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$$\begin{gathered} \mathrm{As} \mathrm{ABEF} \mathrm{is} \mathrm{a} \mathrm{rectangle}, \mathrm{hence}: \\ \mathrm{AB}=\mathrm{EF}=10 \mathrm{cm} \\ \mathrm{ED}=\mathrm{FD}-\mathrm{EF}=16-10=6 \mathrm{cm} \\ \mathrm{AF}=\mathrm{BE}=12 \mathrm{cm} \\ \mathrm{EC}=12-7.5=4.5 \mathrm{cm} \\ \mathrm{Area} \mathrm{of} △\mathrm{ECD}=\frac{1}{2}\times \mathrm{EC}\times \mathrm{ED} \\ =\frac{1}{2}\times 4.5\times 6 \\ =13.5 {\mathrm{cm}}^2 \\ \mathrm{Area} \mathrm{of} \mathrm{rectangleABEF}=\mathrm{AB}\times \mathrm{AF} \\ =12\times 10 \\ =120 {\mathrm{cm}}^2 \\ \mathrm{Hence} \mathrm{area} \mathrm{of} \mathrm{cross} \mathrm{section} \\ =\mathrm{Area} \mathrm{of} △\mathrm{ECD}+\mathrm{Area} \mathrm{of} \mathrm{rectangleABEF} \\ =120+13.5 \\ =\mathbf{133}\mathbf{.}\mathbf{5}\mathbf{ }{\mathbf{cm}}^{\mathbf{2}}\mathbf{ }\left(\mathbf{Answer}\right) \\ \mathrm{Length} \mathrm{of} \mathrm{cross} \mathrm{section}= 4 \mathrm{m} =400 \mathrm{cm} \\ \mathrm{Hence} \\ \mathrm{Volume}=\mathrm{Area}\times \mathrm{Length} \\ =133.5\times 400 \\ =\mathbf{53400}\mathbf{ }{\mathbf{cm}}^{\mathbf{3}}\mathbf{ }\left(\mathbf{Answer}\right) \\ \mathrm{Weight} \mathrm{of} \mathrm{one} 1 {\mathrm{cm}}^3=6.6 \mathrm{grams} \\ \Rightarrow \mathrm{Weight} \mathrm{of} \mathrm{one} 53400 {\mathrm{cm}}^3=53400\times 66 \\ =3524400 \mathrm{grams} \\ =\mathbf{3524}\mathbf{.}\mathbf{4}\mathbf{ }\mathbf{kg}\mathbf{ }\left(\mathbf{Answer}\right) \end{gathered}$$

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