for Well,
d = 4m
r = 2m
H = 14m
Embankment
R = r + w
(w is the width of the embankment)
Therefore, w = R - r
h = 40cm
= 2/5 m
Volume of well = pi(r^2)H
= 22/7 × 2 × 2 × 14
= 176 cm^3
Volume of embankment = volume of well
Pi(R^2)h - pi(r^2)h = pi(r^2)H
Pi h(R^2 - r^2) = pi(r^2)H
h(R+r)(R-r) = (r^2)H
Substitute the values of R and w
H(r+w+r)(w) = r^2H
2/5 (2r+w)(w) = 2×2×14
(2×2 + w)(w) = 4×14× 5/2
(4+w)w = 140
w^2 + 4w -140 = 0
w^2+14w - 10w - 140 = 0
(w+14)(w-10) = 0
w+14=0 w-10=0
w = - 14 w = 10
Therefore width of embankment is 10 m
