Question

a well if inner diameter 14 m is dug . the earth out is spread evenly all around the well to form a 40 cm high embankment. find the width of the embankment
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Answer 1

Answer:

Step-by-step explanation:

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

Hope it helps...