Question

A cuboidal block of solid iron has dimensions 50 cm, 45 cm and 34 cm. How many cuboids of size 5 cm by 3 cm by 2 cm can be obtained from this block? Assume cutting causes no wastage.

Answer 1

$$\begin{gathered} \mathrm{Dimension}\mathrm{of}\mathrm{the}\mathrm{cuboidal}\mathrm{iron}\mathrm{block}=50\mathrm{cm}\times 45\mathrm{cm}\times 34\mathrm{cm} \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{iron}\mathrm{block}=\mathrm{length}\times \mathrm{breadth}\times \mathrm{height}=(50\times 45\times 34){\mathrm{cm}}^3=76500{\mathrm{cm}}^3 \\ \mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{the}\mathrm{dimension}\mathrm{of}\mathrm{one}\mathrm{small}\mathrm{cuboids}\mathrm{is}5\mathrm{cm}\times 3\mathrm{cm}\times 2\mathrm{cm}. \\ \mathrm{Volume}\mathrm{of}\mathrm{one}\mathrm{small}\mathrm{cuboid}=\mathrm{length}\times \mathrm{breadth}\times \mathrm{height}=(5\times 3\times 2){\mathrm{cm}}^3=30{\mathrm{cm}}^3 \\ \therefore \mathrm{The}\mathrm{required}\mathrm{number}\mathrm{of}\mathrm{small}\mathrm{cuboids}\mathrm{that}\mathrm{can}\mathrm{be}\mathrm{obtained}\mathrm{from}\mathrm{the}\mathrm{iron}\mathrm{block}=\frac{\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{iron}\mathrm{block}}{\mathrm{volume}\mathrm{of}\mathrm{one}\mathrm{small}\mathrm{cuboid}}=\frac{76500{\mathrm{cm}}^3}{30{\mathrm{cm}}^3}=2550 \end{gathered}$$