Question

A well of diameter 4m is dug 14m deep. the earth taken out is spread evenly all around the well to form a 40cm high embankment . Find the width of the embankment......in this hoe to find the volume of the embankment?

Answer 1

Answers

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=
$\pi {r}^{2} h$


=((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