. A well of inner diameter 21 m is dug to a depth of 15 m. The earth dug out was evenly spread all around it to a width of 3.5 m to form an embankment. Find the height of embankment formed. (The outer radius of the embankment is 10.5 +3.5 = 14 m and its inner radius is 10.5 m.) "
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Verified answer
Answer:
135m.
Explanation
Let the height of the embankment be 'h' meter.
Given:
Inner Diameter of the well= 21 m
Inner Radius of the well (r) = D/2 = 21/2 m = 10.5 m
Height of the well(h) = 15 m
width= 3.5 m
Outer radius = Inner radius + width = 10.5+3.5 = 14m
Area of the embankment = Outer area - Inner Area
= πR²-πr² = π(R²-r²)
=π(14x14-(21/2)²)
=(22/7)(196-(441/4)) Take L.C.M it's better
=(22/7)(784-441)/4
=22x343/7x4
=7546/28
=269.5m²
Next, we need the volume of earth taken out from the ground
V=πr²h
=(22/7)(21/2)²x15
=22*441*15/4
=145530/4
=36382.5m³
Height of embankment
= Volume of earth dug out/ Area of the embankment
=36382.5m³/269.5m² = 135m.
∴Height of embankment = 135m
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