Question

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

Answer 1

Length of the cuboid (l) = 21 cm

Breadth of the cuboid (b) = 9 cm

Height of the cuboid (h) = 8 cm

$\text{Volume of cuboid}=21\times 9\times 8=1512\text{cu cm.}$

$\text{No. of cubes that can be cut along the length}=\frac{21}{3}=7$

$\text{No. of cubes that can be cut along the breadth}=\frac{9}{3}=3$

$\text{No. of cubes that can be cut along the height}=\frac{8}{3}=2.6$

Along the height we can cut only 2 pieces and remaining is waste.

$\therefore \text{Total number of cubes cut}=7\times 3\times 2=42$

$\text{Volume of each cube}=3\times 3\times 3=27{\text{cm}}^3$

$\text{Volume of all cubes}=27\times 42$

$=1134{\text{cm}}^3$

$\therefore \text{Volume of the waste wood}=1512–1134=378{\text{cm}}^3$