Question

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

Answer 1

{some correction in question}

Question : A well of diameter 3 m is dug 14 m deep. The earth/soil taken out it has been spread evenly all around it in the shape of a circular ring of width 4 m to form on embankment. The height of the embankment ?

Solution : Assume that, the shape of well and embankment is cylindrical.

Now, according to question,

• diameter of well = 3 m
• radius of well, r = diameter/2 = 3/2 = 1.5 m
• height/depth of well, h = 14 m

• width of embankment = 4m
• Length of embankment with radius of well, R = 4 + 1.5 = 5.5 m
• height of embankment, H ?

Here, we know; the earth/soil taken out it has been spread evenly all around it in the shape of a circular ring of width 4 m to form on embankment.

Hence, we know that volume of embankment is equal to volume of well.

⟹ volume of embankment = volume of well

⟹ π * [(R)² - (r)²] * H = π * (r)² * h

⟹ [(R)² - (r)²] * H = (r)² * h

⟹ [(5.5)² - (1.5)²] * H = (1.5)² * 14

⟹ [30.25 - 2.25] * H = 2.25 * 14

⟹ 28 * H = 31.5

⟹ H = 31.5/28

⟹ H = 1.125 m

Answer : Hence, height of the embankment is 1.125 m.