Question

# In order to fix an electric pole along a roadside, a pit with dimensions $50cm \times 50cm$ is dug with the help of a spade. The pit is prepared by removing earth by $250$ strokes of spade. If one stroke of spade removes $500$ $c{m^3}$ of earth, then what is the depth of the pit?

Hint:In this question let us suppose that the depth of the pit is x . Now try to find out the volume of dig in term of x that is equal to $50cm \times 50cm \times xcm$ and is given that the one stroke of spade removes $500$ $c{m^3}$so find out what amount of earth is dig in $250$ strokes of spade now compare both the equation and get the x.

First let us suppose that the depth of the pit is x .
We know that the shape of the pit is in cuboids shape
Hence the volume of the cuboids is length $\times$ breadth $\times$ depth .
It is given that the length $\times$ breadth = $50cm \times 50cm$ and depth of the pit is equal to x .
hence the volume of pit is equal $50cm \times 50cm \times xcm$
that is equal to $2500x$ $c{m^3}$
So the volume of the pit is $2500x$ $c{m^3}$
Now we have to calculate the volume of the pit from some other method as it is given in the question that the one stroke of spade removes $500$ $c{m^3}$ .
And it is also given that $250$ strokes of spade is required for the removal of the earth .
Hence total volume removed by pit is equal to No of stokes $\times$ Volume removed in one stokes
that is equal to $500 \times 250c{m^3}$
Now we have to equate both the volumes i.e volume of pit and volume removed through pit
Volume of Pit = Total volume of removed through pit
$2500x = 500 \times 250$
Hence $x = \dfrac{500 \times 250}{2500}$
$x = \dfrac{500}{10}$
$x = 50$ cm
Hence the depth of the pit is $x = 50$ cm

Note:Volume refers to the amount of space the object takes up. In other words, volume is a measure of the size of an object, just like height and width are ways to describe size.In the question volume refers to what amount of earth is removed or what amount of earth the pit is held .In cube all the sides are equal in length and its Volume is equal to ${l^3}$ where l is the side of the cube .