(Q13).A well of diameter 14 m is dug 15 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 7 m to form an embankment. Find the height of the embankment

Answer:

Volume of the well = Volume of the embank

Volume of the cylinder = Volume of the embank

Cylinder :

Radius r =
d
2
=
= cm

Height/depth, h = 15 m

Volume V = πr2h

=
× × ×

= × ×

= m3

Embank:

image

Let the height of the embank = h m

Inner radius ‘r’ = Radius of well = 7 m

Outer radius, R = inner radius + width

= m + m = m

Area of the base of the embank = (Area of outer circle) – (Area of inner circle)

= πR2 – πr2

= π(R2 – r2)

=
()
=
× (+) × (-)
=
× ×

= m2

∴ Volume of the embank = Base area × height

= × = m3

m3 = m3

h =
= m.