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Question
A well of diameter 4 m is dug 14 m deep the earth taken out is spread evenly all around the well to form embankment .find the width of enbakment.
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Solution
You are not given the height of the embankment in the question... Only then answer can be found...
I have taken that height =40cm...
Now
Let h be the height of well and r be the radius of well
h=14m,r=d/2=2m
Volume of earth taken out after digging the well= pi*r² * h
=((22/7)*2*2*14)m³=176m³
Let x be the width of embankment formed by using(i)
Total width of well including embankment (R)=2+x
Height of embankment(H)=40cm=40/100m
Volume of well=Volume of embankment
So,
Volume of embankment=pi*(R²-r²)H=176
=(22/7)*[(2+x)²-(2)²]*(40/100)=176
(44/35)[x²+4x]=176
44x²+176x=6160
x²+14x-10x-140=0
x(x+14)-10(x+14)=0
(x+14)(x-10)=0
X+14=0 or x-10=0
X=-14 or x=10
Therefore,width of embankment=10m
I have taken that height =40cm...
Now
Let h be the height of well and r be the radius of well
h=14m,r=d/2=2m
Volume of earth taken out after digging the well= pi*r² * h
=((22/7)*2*2*14)m³=176m³
Let x be the width of embankment formed by using(i)
Total width of well including embankment (R)=2+x
Height of embankment(H)=40cm=40/100m
Volume of well=Volume of embankment
So,
Volume of embankment=pi*(R²-r²)H=176
=(22/7)*[(2+x)²-(2)²]*(40/100)=176
(44/35)[x²+4x]=176
44x²+176x=6160
x²+14x-10x-140=0
x(x+14)-10(x+14)=0
(x+14)(x-10)=0
X+14=0 or x-10=0
X=-14 or x=10
Therefore,width of embankment=10m
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