Question

A plot of land in the form of rectangle has dimension 240m x 280m. A drainlet 10m wide is dug around it (on the outside) and the earth dug out evenly spread out over the plot increasing its surface level by 25cm. Find the depth of the drainlet.

Answer 1

Hope it helps

Since the rectangular surface level is increased, we can calculated the volume of earth dug and added on the rectangular plot.Volume of earth dug = 240m x 180m x 0.25m = 10800 m3 This volume is also the volume of the drainlet.= 2(240m x 10m x d m) + 2(180m x 10m x d m) = 10800 m3.d = depth = 1.29 m

Answer 2

let the depth of the drainlet be X
l,b,h of side 1 = 260,10,X
l,b,h of side 2 = 180,10,X
total volume of the drainlet = 2(volume of side 1) = 2(volume of side 2)
= 5200x + 3600x = 8800x m3
​when earth dug out is evenly spread over the plot,we get a cuboid whose base is 240 * 180m2​ and height = 25ch = 0.25m
so............... volume of earth spread over the plot = 240*180*0.25 = 10800m3
​as per the ques......volume of earth spread over the plot = volume of drainlet..........
10800 = 8800x
x =1.227m