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  # 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?
  
  Last updated date: 03rd Aug 2024
  Total views: 426.6k
  Views today: 12.26k
  Verified
  426.6k+ views
  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 .
explanation: The document contains a math question and a detailed solution to the problem. The question asks for the depth of a pit given the dimensions of the pit and the volume of earth removed per spade stroke. The solution calculates the depth step-by-step.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
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  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
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  # 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?
  
  Last updated date: 03rd Aug 2024
  Total views: 426.6k
  Views today: 12.26k
  Verified
  426.6k+ views
  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 .
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and a detailed solution to the problem. The question asks for the depth of a pit given the dimensions of the pit and the volume of earth removed per spade stroke. The solution calculates the depth step-by-step.
  
  Label: question-and-answer