A rectangular tank measuring 5m x 4.5m×2.1m is dug in the centre of the field measuring 13.5 m×2.5 m .The earth dug out is spread evenly over the remaining portion of the field .How much is the level
of the field raised?
Answers
Ans: 1.94 metre
Volume of earth dug out
= volume of the rectangular tank
= 5 × 4.5 × 2.1
= 47.25 m3
Given that length and breadth of the field are 13.5 m and 2.5 m respectively.
Therefore, (5 m × 4.5 m) cannot be the length and breadth of the rectangular tank because the breadth of the tank must be lesser than 2.5 m (as the tank is inside the field)
Therefore, assuming that the volume of the tank is expressed as height × length × breadth and taking
length of the tank as 4.5m, breadth of the tank = 2.1m and height of the tank = 5m
Area of the field = 13.5 × 2.5 = 33.75 m
Area of the top face of the tank = 4.5 × 2.1 = 9.45 m
Area of the remaining portion of the field = 33.75 - 9.45 = 24.3 m2
earth dug out is spread evenly over this remaining portion of the field.
Suppose level of the field is raised by
x
metre.
Then, volume of this earth
=
24.3
×
x
Now we have,
47.25
=
24.3
×
x
x
=
47.25
24.4
=
1.94
metre
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