# a trench 3 m wide and 2 m deep is dug all round inside a rectangular plot 46m by 36 n and the earth dugout is spread on the remaining portion . by how much will the level of the earth be raised

Given trench 3 m wide and 2 m deep is dug all round inside a rectangular plot 46 m by 36 m , SO we have our diagram , As :

So , Length of trench  = 46 + 46 + ( 36 - 3 - 3 ) + ( 36 - 3 - 3 ) = 92  + 30 + 30 =  152 m

We know Volume of cuboid  =  Length $×$ Breadth $×$ Height or deapth

Here Volume of dugout earth  =  Volume of trench
So,
Volume of our trench  =  152 $×$ 3 $×$ 2  =  912 m3

Now Length of remaining portion of plot  = 46 - 3 - 3  =  40 m
And
Breadth of remaining portion of plot  = 36 - 3 - 3  =  30 m

Let the level of the earth be raised =  h  .

And Volume of remaining portion with raised height  =  Volume of dugout earth .

So, we get

40 $×$ 30 $×$ h  =  912

1200 h  =  912

h  = 0.76 m

We know 1 m  =  100 cm , So

0.76 m  = 76 cm

So,
The level of the earth be raised =  76 cm                                                ( Ans )

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