Q30 of 47 Page 1

A well of diameter 4 m is dug 14 m deep. The earth taken out is spread evenly all around the well to form a 40 cm high embankment. Find the width of the embankment.

Given, Diameter of well = 4m

So, radius of well(r) = 4/2 = 2m


Height of well(h) = 14m



Let the width of the embankment = x m


Total width of well including embankment(R) = (2 + x)m


Height of the embankment(H) = 40cm = 0.4m


Volume of the earth out =


⇒


⇒ 140 = (2 + x)2-4


⇒ (x + 2)2-144 = 0


⇒ (x + 2)2-122 = 0
⇒ (x + 2 + 12)(x + 2-12) = 0


⇒ (x + 14)(x-10) = 0


⇒ x = -14(Rejected) or x = 10


∴ The width of the embankment = 10m


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