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A field is $60$m long and $20$m wide. A tank $12$m long, $10$m broad and $3$m deep is dug in the field. The earth taken out of it is spread evenly over the field. How much is the level of the field raised supporting the earth taken out increases by $\dfrac{1}{8}$ of the volume?

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Last updated date: 22nd Jun 2024
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Answer
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Hint: We are given a field in which a tank is dug out the earth taken out of the field is evenly spread over the field we have to find how much the level of the field raised by the spreading of the earth in this type of problem first we will find the area of field and then we will find the area of tank then we will find out the area of field on which earth needs to be spread then we will find the area of remaining field and the volume of earth taken out from the tank then we will find the height raised.

Formula used: Volume = L×B×H
Here L= Length, B= breadth, H= height
Area = $L \times B$
Here L = Length B = breadth

Complete step-by-step answer:
Step1: We are given field of dimensions length$ = 60$m breadth$ = 20$m
And dimensions tank i.e. dug out is
Length$ = 12$m, breadth$ = 10$m, height$ = 3$m
Step2: Firstly we will find the area of the field using the formula
Area = L×B
Here L$ = 60$m, B$ = 20$m
Substituting the value in formula we get:
Area$ = 60 \times 20$
          $ = 1200$m2
Area of the tank dug out is
Area = L × B
Here L$ = 12$m and B$ = 10$m
 Area$ = 12 \times 10$
Area of tank$ = 120$$m^2$
Step3: Then we will the area of the field where the earth has to be spread
= (Area of field) - (area tank)
On substituting the value we get
On $ = 1200 - 120$
      $ = 1080$$m^2$
Step4: Then we will find the volume of the earth dug out for it
V = L×B×H
Here L$ = 12$m, B$ = 10$m, H$ = 3$m
Substituting the value in the formula
V $ = 12 \times 10 \times 3$
V$ = 360$$m^3$
Step5: Volume of earth that is to be spread = Volume of earth dug out + $\dfrac{1}{8}$(volume of earth dug)$ = 360 + \dfrac{1}{8}(360)$
On solving the equation
$ = 360 + 45$
Adding the number we get
 $ = 405$$m^3$
Then we will find the height of the field raised for it and we will use the formula
 H= $\dfrac{{Volume}}{{Area}}$
 Here V$ = 405$$m^3$
 Area$ = 1080$$m^2$
Substituting the value in the formula we get:
Area$ = \dfrac{{405}}{{1080}}$
         $ = 0.375$m

The height is $0.375$m

Note: Don’t get confused in applying the formula or where to apply the formula and which one to find the height of we always divide volume by area this should be kept in mind and in case of finding the volume earth dug out it is always equal to the volume of the tank and in all such case.