Question

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?​

Answer 1

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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