Question

An 8 m long cuboidal beam of wood when sliced produces four thousand 1 cm cubes and there is no wastage of wood in this process. If one edge of the beam is 0.5 m, find the third edge.

Answer 1

Length of the wooden beam = 8 m 

Width = 0 . 5 m 

Suppose that the height of the beam is h m . 

\[\text { Then, its volume = length  }\times \text { width } \times \text { height  }= 8 \times 0 . 5 \times h = 4 \times h m^3 \]

\[\text { Also, it produces 4000 cubes, each of edge 1 cm = 1  }\times \frac{1}{100}m = 0 . 01 m (100 cm = 1 m)\]

\[\text { Volume of a cube = (side ) }^3 = (0 . 01 )^3 = 0 . 000001 m^3 \]

\[ \therefore \text { Volume of 4000 cubes =} 4000 \times 0 . 000001 = 0 . 004 m^3 \] 

\[\text { Since there is no wastage of wood in preparing cubes, the volume of the 4000 cubes will be equal to the volume of the cuboidal beam }. \]

\[\text { i . e . , Volume of the cuboidal beam = volume of 4000 cubes }\]

\[ \Rightarrow 4 \times h = 0 . 004\]

\[ \Rightarrow h = \frac{0 . 004}{4} = 0 . 001 m\]

\[ \therefore \text { The third edge of the cuboidal wooden beam is 0 } . 001 m .\]