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144. (a) A field is 90 metres long and 50 metres broad. A 25-metre long, 20-metre broad and 4-metre deep tank dug in the field and the earth taken out is spread evenly over the remaining field. How much will the level of the field rise?

Answer :

To determine how much the level of the field will rise after the earth from the tank is spread evenly over it, follow these steps:

  1. Calculate the Volume of the Tank:

    The volume of the tank can be calculated using the formula for the volume of a rectangular prism:

    [tex]V = \, \text{length} \times \text{breadth} \times \text{depth}[/tex]

    Substituting the given dimensions:

    [tex]V =\, 25 \, \text{m} \times 20 \, \text{m} \times 4 \, \text{m} = 2000 \, \text{cubic meters}[/tex]

  2. Calculate the Area of the Remaining Field:

    First, find the total area of the field:

    [tex]\text{Total area} = 90 \, \text{m} \times 50 \, \text{m} = 4500 \, \text{square meters}[/tex]

    Subtract the area of the tank:

    [tex]\text{Area of the tank} = 25 \, \text{m} \times 20 \, \text{m} = 500 \, \text{square meters}[/tex]

    Remaining area:

    [tex]\text{Remaining area} = 4500 \, \text{sq m} - 500 \, \text{sq m} = 4000 \, \text{square meters}[/tex]

  3. Determine the Rise in Level of the Field:

    To find out how much the level of the field will rise, we use the volume of the earth that came from the tank (which is 2000 cubic meters) and spread it over the remaining 4000 square meters of the field:

    [tex]\text{Rise in level} = \frac{\text{Volume of earth}}{\text{Area over which it's spread}} = \frac{2000 \, \text{cubic meters}}{4000 \, \text{square meters}}[/tex]

    [tex]\text{Rise in level} = 0.5 \, \text{meters}[/tex]

Therefore, the level of the field will rise by 0.5 meters.

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