Question

A cube of metal of 6 cm edge is melted and cast into a cuboid whose base is $9cm\times 8cm$. Find the height.

Answer 1

Hint: As given in the question a cube is melted and cast into a cuboid so the volume of the cube and cuboid must be the same. So we will equate volumes of both cube and cuboid and substitute the values. Then simplifying the obtained equation will give the desired answer.

Complete step by step solution:
We have been given that a cube of metal of 6 cm edge is melted and cast into a cuboid whose base is $9cm\times 8cm$.
We have to find the height of the cuboid.
Now, the cube is melted and cast into a cuboid so the volume of the cube and cuboid will be the same.
So we will get
$\text{volume of cube = volume of cuboid}$

Now, we know that the volume of cube will be ${{a}^{3}}$, where a is the edge of cube
Also the volume of cuboid will be $l\times b\times h$, where l is the length of cuboid, b is the width of cuboid and h is the height of cuboid.
Now, substituting the values we will get
$\begin{align}
  & \Rightarrow {{a}^{3}}=l\times b\times h \\
 & \Rightarrow {{6}^{3}}=9\times 8\times h \\
\end{align}$
Now, simplifying the above obtained equation we will get
$\begin{align}
  & \Rightarrow 216=72h \\
 & \Rightarrow \dfrac{216}{72}=h \\
 & \Rightarrow h=3cm \\
\end{align}$
Hence we get the height of the cuboid as 3 cm.

Note: The point to be remembered is that the cube and cuboid look the same in the structure but they have different properties. A cube has 6 square shaped faces but a cuboid has rectangular shaped faces. All the sides of a cube have the same measure but the cuboid has different length, width and height.