Question

a well of diameter 3 m is dug 14 m deep . The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment . find the height of the embankment.​

Answer 1

Answer:

Step-by-step explanation:

Diameter =3m

Radius=3/2m

Height=14m

Well is in the form of cylinder. If earth is taken out of to form a embankment

Hence,

Volume of cylinderical well=volume of embankment

Width of embankment=4m

Total radius =4+3/2 m=11/2m

Volume of cylinder=volume of embankment

πr²H=π(R²-r²)h

3/2×3/2×14=(11/2+3/2)(11/2-3/2)h

[a²-b²=(a+b)(a-b)]

3/2×3/2×14=14/2×8/2×h

By solving it

h=9/8m

Answer 2

Answer:

1.125 m

Step-by-step explanation:

• Cylinderical well:-

1.  r = 3 / 2 m
2. h= 14 m

• Embankment:-

1. width=4 m
2. R=3/2 +4= 11/2 m(BIGGER RADIUS)
3. r= 3/2 m(SMALLER RADIUS)

Volume of well = Volume of Embankment

$\pi r^{2}h = \pi (R^{2}-r^{2}  )h$

(3/2)² * 14 = (11/2 + 3/2)(11/2 - 3/2)h

9/4 * 14 = 14/2 * 8/2 * h

9/2 * 7 = 7 * 4 * h

(9/2) / 4 = h

h=9/2 * 1/4

h= 1.125 m

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