# a plot of land is in the form of a rectangle has dimensiond 240cm X 180cm. a drainlet 10m wide is dug all around and the earth dug out is evenly spread over the plot increasing its surface level by 25cm. find the depth of the drainlet.

Consider the figure,

Here, for the rectangular plot;
Length (l) = 240 cm
Now, the earth dug out from the drainlet is evenly spread out over the plot. So,
Height (h1) = 25 cm
Volume (V) = l*b*h1
= 240*180*25
= 1080000 cm3
Now, let the depth of the drainlet be h.
Volume of the earth dug out = Volume of EMPH+ Volume of NFGO + Volume of BPOC + Volume of AMND
= (260*10*h) + (260*10*h) + (180*10*h) + (180*10*h)
= 2600h + 2600 h +1800 h + 1800h
= 8800 h
Next, as the earth dug out is evenly spread over the plot, So
Volume of earth dug out = Volume of the rectangular plot
$8800h=1080000\phantom{\rule{0ex}{0ex}}h=\frac{1080000}{8800}\phantom{\rule{0ex}{0ex}}h=122.73$

Therefore, the depth of the drainlet is 122.73 cm

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