A low land of length 40m and breadth 30m is to make 2.5dm high by soil. For this the amount of soil required is obtained from a trench round the land of 2.5m broad. Find the depth of the trench.
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See the attachment for the rough sketch. The blue area is the land (40m × 30m)
The yellow marked area is the trench of width 2.5m
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Area of land (blue rectangle) = 40×30 = 1200 m^2
Height to be raised = 2.5dm = 25cm = 0.25 m
Volume of soil needed = area × height = 1200 × 0.25 = 300 m^3
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Now 300m^3 soil will be taken from the trench outside the land.
width of trench = 2.5m
Dimensions of trench:(red rectangle)
So total length of trench = 40 + 2.5 + 2.5 = 45m
total width = 30+2.5+2.5 = 35 m
Area of trench(yellow area) = area of red rectangle - area of blue rectangle
= 45×35 - 40×30
= 1575 - 1200
=> Area of trench = 375 m^2
Let the depth of trench = d
Volume of soil = area of tench × depth
=> 300 = 375 × d
=> d = 300 / 375
=> d = 4/5 m
=> d = 0.8m = 80cm
Depth of trench is 80cm
The yellow marked area is the trench of width 2.5m
_____________________________
Area of land (blue rectangle) = 40×30 = 1200 m^2
Height to be raised = 2.5dm = 25cm = 0.25 m
Volume of soil needed = area × height = 1200 × 0.25 = 300 m^3
_____________________________
Now 300m^3 soil will be taken from the trench outside the land.
width of trench = 2.5m
Dimensions of trench:(red rectangle)
So total length of trench = 40 + 2.5 + 2.5 = 45m
total width = 30+2.5+2.5 = 35 m
Area of trench(yellow area) = area of red rectangle - area of blue rectangle
= 45×35 - 40×30
= 1575 - 1200
=> Area of trench = 375 m^2
Let the depth of trench = d
Volume of soil = area of tench × depth
=> 300 = 375 × d
=> d = 300 / 375
=> d = 4/5 m
=> d = 0.8m = 80cm
Depth of trench is 80cm
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