A carpenter makes a letter box which has a volume of \[13400c{m^3}\]. The base has an area of \[670c{m^2}\]. What is the height of the box?

Hint: For the given question we need to find the height of the box, as the box may be in the shape of cube or cuboid as with the given in the question of the details as volume and area, we could able to find the height of the letter box made by the carpenter.
Formula Used:
Volume of a box = Area of base \[ \times \] height

Complete step-by-step answer:
In this problem,
We are given that,
Volume of the box = \[13400c{m^3}\]
Area of base of the box = \[670c{m^2}\]
Let the height of the box be h.
\[\therefore \]Volume of a box = Area of base \[ \times \] height
\[\because \]\[13400 = 670 \times h\]
\[ \Rightarrow h = \dfrac{{13400c{m^3}}}{{670c{m^2}}}\]
On further simplification, we get
\[ \Rightarrow h = \dfrac{{1340}}{{67}}cm\]
\[h = 20cm\]
Hence, the height of the box is \[20cm\].
So, the correct answer is “\[20\;cm\]”.

Note: A rectangular cuboid is similar to a cube but does not have three equal-length edges. In boxes, the rectangular cuboid shape is common.
A rectangle and a cuboid differ primarily in that one is a 2D shape and the other is a 3D shape.
The basic difference between a cube and a cuboid is that a cube has the same length, height, and width, whereas cuboids may or may not have these three dimensions. A right rectangular prism is another name for the cuboid.