a plot of land in the form of rectangle has a dimension 240m x 180m . a draiinlet 10m 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 25cm . find the depth of the drainlet.
Answers
Answer:
1.227 m
Step-by-step explanation:
Given : Length = 240 m, Breadth = 180 m, Height = 25 cm = 0.25 m.
Volume of the plot = 240 * 180 * 0.25
= 10800 m³.
Given, earth dug out is evenly spread over the plot, increasing by 25 cm.
Let the depth of the drainlet = d cm.
∴ Volume of the drainlet = (2 * 260 * 10 * d) + (2 * 180 * 10 * d) m³
= (5200 + 3600) * d
= 8800 * d m³
Now,
Volume of the plot is equal to the volume of the drainlet
= 10800 m³ = 8800 * dm³
⇒ 10800/8800 = d
⇒ 1.227 m = d
Therefore, depth of the drainlet = 1.227 m.
Hope it helps!
Step-by-step explanation:
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