Question

13. A plot of land in the form of rectangle has dimensions
250 mx 160. A drain 10 m side is dug all around it and the earth
dug out is evenly spread over the plot increasing its surface
level by 40 cm. Find the depth of the drain.
​

Answer 1

$\sf\large\underline{Given:}$

• $\tt{Length\:_{(rectangle)}=250m}$
• $\tt{Breadth\:_{(rectangle)}=160m}$
• $\tt{Drain\:_{(dug\:in\: earth)}=10m\:all\: side}$
• $\tt{The\:plot\: increasing\: it's\: surface\: level=40cm=0.40m}$

$\sf\large\underline{To\: Find:}$

• $\tt{The\: drain\:_{(depth)}=?}$

$\sf\large\underline{Solution:}$

• At first calculate the the area of drain where the drain is dug out. Here, volume of cubiod is equal to the volume of plot.]

$\tt{\implies Outer\:_{(length)}=250+2*10=270m}$

$\tt{\implies Outer\:_{(breadth)}=160+2*10=180m}$

$\tt{\implies Outer\:_{(area)}=270*180}$

$\tt{\implies Outer\:_{(area)}=48600m^2}$

• calculate Inner area of plot here]

$\tt{\implies Inner\:_{(area)}=250*160}$

$\tt{\implies Inner\:_{(area)}=40000}$

• Now, calculate the area of drain ]

$\tt{\implies Area\:_{(drain)}=Outer\:_{(area)}-Inner\:_{(area)}}$

$\tt{\implies Area\:_{(drain)}=48600-40000}$

$\tt{\implies Area\:_{(drain)}=8600m^2}$

• Let, the depth of drain be x here

$\sf\large\underline{Formula\: used\:here:}$

$\tt{\implies Volume\:_{(drain)}=l*b*h}$

$\tt{\implies Area\:_{(drain)}*depth=Volume\:_{(drain)}}$

$\tt{\implies 8600\times\:x=250*160*0.40}$

$\tt{\implies 8600x=16000}$

$\tt{\implies x=1.86m}$

$\sf\large{Hence,}$

$\bf{\implies The\:depth\:_{(drain)}=1.86m}$

Answer 2

• Given
• width of the drainlet = 10m
• Let depth of the drainlet be = x

• volume of the earth dug out

$\leadsto v1+v2+v3+v4\\ \leadsto 2×v1+2×v4$ ( v= volume )

$\rightarrow 2[l×b×h] +2 [l×b×h]\\ \rightarrow 2[270×10×x] +2 [160×10×x]\\ \rightarrow 5400x+3200x$

• Volume of earth dug out = $8600xm^3$

$\rule{230}2$

• Volume of the plot cuboid = l×b×h

→ 250×160×10 (250 & 160 are in metre ) so, changing 40 cm into metre.

$\rightarrow 250×160×0.40m\\ \rightarrow 16000 m^3$

• we know,
• volume of plot cuboid = volume of earth dug out.

→ 8600x=16000

→ x=$\huge\frac{ 16000}{8600}$

→ x = 1.86m

$\rule{230}2$

• Hence,

• Depth = 1.86m