Question

How many cubes of side $3cms$ each can be cut from wooden block in the form of a cuboid whose length, breadth and height are $21cm,9cm$ and $8cm$ respectively. How much volume of wood is wasted?

Answer 1

Length of the cuboid $\left(l\right)=21cm$
Breadth of the cuboid $\left(b\right)=9cm$
Height of the cuboid $\left(h\right)=8cm$
Volume of cuboid $=21\times 9\times 8=1512cucm$
No. of cubes that can be cut along the length $=\frac{21}{3}=7$
No. of cubes that can be cut along the breadth $=\frac{9}{3}=3$
No. of cubes that can be cut along the height $=\frac{8}{3}=2.6$
Along the height we can cut only $2$ pieces and remaining is waste.
$\therefore$ Total number of cubes cut $=7\times 3\times 2$
$=42$
Volume of each cube $=3\times 3\times 3=27c{m}^3$
Volume of all cubes $=27\times 42$
$=1124c{m}^3$
$\therefore$ Volume of the waste wood $=1512-1124=388c{m}^3$