Question

A pit $5m$ long and $3.5m$ wide is dug to a certain depth. If the volume of earth is taken to be $14{m^3}$ then what is the depth of the pit?

Answer 1

Hint:
A length is given equal to $5m$ and the breadth is $3.5m$ and let the depth be $x$ then the volume of the earth would be taken to be ${\text{length}} \times {\text{breadth}} \times {\text{height}}$ and here ${\text{length}} \times {\text{breadth}}$ gives the area of the surface of the pit.

Complete step by step solution:
Here in this question pit is used which means the hollow or indentation in the surface. The surface of the earth is taken out up to a certain depth and the pit is formed in the form of the cuboid where length and breadth are given in the question and here cuboid is the three dimensional figure.
Here volume is given by the ${\text{area of the surface}} \times {\text{depth}}$
Here we are given that the volume of the earth taken out is $14{m^3}$ and we need to find the depth of the pit. Now let us assume that the depth of the pit is $x{\text{ meter}}$ and now we know that the volume of the earth taken out will be equal to the product of the area of the surface and the depth up to which the earth is taken out. So let us find the area of the pit. As we are given that the area of the pit will be ${\text{length}} \times {\text{breadth}}$ and length is given as $5m$ and the breadth as $3.5m$
So ${\text{area of the surface}} = {\text{length}} \times {\text{breadth}}$
$
   = 5(3.5) \\
   = 17.5{m^2} \\
 $
Now we are also given that the volume of the earth dig is $14{m^3}$
${\text{volume of earth taken out}} = {\text{area of the surface}} \times {\text{depth}}$
$
  14{m^3} = 17.5{m^2}(x) \\
  x = \dfrac{{14}}{{17.5}} = 0.8m \\
 $

Hence depth of the pit is $0.8m$.

Note:
We should know the volume of different shapes like ${\text{volume of cuboid}} = {\text{length}} \times {\text{breadth}} \times {\text{height}}$
${\text{volume of the cube}} = {({\text{length)}}^3}$
${\text{volume of cylinder}} = \pi {r^2}h$ and so on