Question

How many cubic blocks of wood of side 20cm can be cut from a block of wood having dimensions of 2m, 80cm and 40cm?

Answer 1

Hint: This is the formula for the volume of a block of wood having different dimensions.
\[Volume{\text{ }} = {\text{ }}length\; \times \;width\; \times height\]
And volume of a block of wood having same dimensions is \[Volume{\text{ }} = {\text{ }}length\; \times \;length\; \times length\]
And after calculating the volumes of cubes and cuboid, one can check the number of cubes present in cuboids.

Complete step by step solution: When you look around the room in your house, you can see many objects that have the shape of a rectangular box. For example, furniture, books and TV are in the shape of a rectangular box. This shape is a cuboid. On the other hand, objects such as ice, dice and Rubik’s cube are examples of another 3D shape called a cube. As a matter of fact, a cube is a special type of cuboid in which all sides are squares and identical. Let us do it for cubes and cuboids. Here in this question, the bigger block of wood will be acting as a cuboid and smaller ones will be acting as cubes.
As we know, there are different lengths of all the sides of the given bigger wooden block, so it will be having the shape of a cuboid. Therefore,
\[\begin{array}{*{20}{l}}
  {Length{\text{ }}of{\text{ }}Wooden{\text{ }}Block{\text{ }} = {\text{ }}2m{\text{ }} = {\text{ }}2{\text{ }} \times {\text{ }}100{\text{ }} = {\text{ }}200cm} \\
  {Width{\text{ }}of{\text{ }}Wooden{\text{ }}Block{\text{ }} = {\text{ }}80cm} \\
  {Height{\text{ }}of{\text{ }}Wooden{\text{ }}Block{\text{ }} = {\text{ }}40cm}
\end{array}\]
\[\begin{array}{*{20}{l}}
  {Volume{\text{ }}of{\text{ }}block{\text{ }}of{\text{ }}wood{\text{ }} = {\text{ }}200cm{\text{ }} \times {\text{ }}80cm{\text{ }} \times {\text{ }}40cm{\text{ }} = {\text{ }}64000cm{\text{ }}cube} \\
  {Volume{\text{ }}of{\text{ }}1{\text{ }}cubical{\text{ }}block{\text{ }} = {\text{ }}20cm{\text{ }} \times {\text{ }}20cm{\text{ }} \times {\text{ }}20cm{\text{ }} = {\text{ }}800cm{\text{ }}cube} \\
  {No.{\text{ }}of{\text{ }}blocks{\text{ }} = 64000 \div 800{\text{ }} = {\text{ }}80{\text{ }}blocks}
\end{array}\]

Note: The total number of given smaller wooden blocks out of the bigger blocks can be calculated by dividing the volume of the bigger block with the volume of the smaller one.