Question

How many 3 metres cube can be cut from a cuboid measuring $ 18m\times 12m\times 9m $ .

Answer 1

Hint: First, before proceeding for this, we must draw both the diagrams: a cuboid with dimensions $ 18m\times 12m\times 9m $ and a cube with dimensions 3 metres. Then, this is only possible by the division of the volume of the cuboid to the volume of the cube as the volume of the figure remains the same after cutting or moulding. Then, by using the formula for the volume of cuboid as $ {{V}_{1}}=l\times b\times h $ and volume of cube as $ {{V}_{2}}={{a}^{3}} $ , we get the final result.

Complete step-by-step answer:
In this question, we are supposed to find the number of 3 metres cube can be cut from a cuboid measuring $ 18m\times 12m\times 9m $ .
So, before proceeding for this, we must draw both the diagrams a cuboid with dimensions $ 18m\times 12m\times 9m $ and cube with dimensions 3 metres as:

Now, we want to get the number of cubes that we can obtain from the cuboid with dimension mentioned above.
So, this is only possible by the division of the volume of the cuboid to the volume of the cube as the volume of the figure remains the same after cutting or moulding.
Now, we must know the formula for the volume of cuboid as $ {{V}_{1}} $ with length l, breadth b and height h as:
 $ {{V}_{1}}=l\times b\times h $
Similarly, we must know the formula for the volume of cube as $ {{V}_{2}} $ with side a as:
 $ {{V}_{2}}={{a}^{3}} $
Now, from the above figure we get the values of l=18m, b=12m, and h=9m.
Similarly, we get the value of a as 3m.
Now, by using the condition stated above, the number n of the cubes cut from cuboid is given by:
 $ n=\dfrac{{{V}_{1}}}{{{V}_{2}}} $
Now, by substituting the values of both the volumes of cuboid and cube, we get:
 $ n=\dfrac{18\times 12\times 9}{{{3}^{3}}} $
Then, by solving the above expression, we get:
 $ \begin{align}
  & n=\dfrac{18\times 12\times 9}{3\times 3\times 3} \\
 & \Rightarrow n=72 \\
\end{align} $
So, the number of cubes with side 3m cut from cuboid with dimensions $ 18m\times 12m\times 9m $ are 72.
Hence, the correct answer is 72.

Note: Now, to solve these type of the question, the only mistake we can occur is by using the formulas of the TSA of cuboid and cube instead of volume of cube and cuboid and most of us get confused with the fact that TSA will not be same after cutting or reshaping but volume remains the same with that. So, be careful about this fact before solving these types of questions.