A plot of land in the form of a rectangle has a dimension `240 m\ x\ 180 m` . A drainlet `10 m` wide is dug all around it (on the outside) and the earth dug out is evenly spread over the plot, increasing its surface level by `25\ c mdot` Find the depth of the drainlet.

Explanation

Outer length (including drainlet) = `(240 + 20)` m= `260` m
Outer breadth (including drainlet) =` (180 + 20) `m =` 200` m
area of the drainlet = ` ( 260 xx200 )m^2 - ( 240 xx180 )m^2 `
` = 52000 m^2 - 43200 m^2 = 8800 m^2`
Let `x` be the depth of the drainlet
Then volume of earth dug out = Volume of earth spread on the land
`8800 xx x = 180 xx 240 xx0.25`
` x = 180 xx240 xx0.25/8800`
` = 27/22 = 1.227 m`