Hence, on comparing the volume of well and the volume of embankment we can find the width of the embankment. Final solution: the width of the embankment when a well of diameter 4m is dug 14m deep. The earth taken out is spread evenly all around the well to form a 40cm high embankment is 7.48m.
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Answer:
Explanation:
Calculate the volume of the well:
Radius (r) = diameter/2 = 4m / 2 = 2m
Volume of well (V_well) = πr²h = π * 2² * 14 = 176 m³
Calculate the volume of the embankment:
Let x be the width of the embankment.
Radius of the outer circle of the embankment = r + x
Volume of embankment (V_embankment) = π((r+x)² - r²)h
Substitute values: V_embankment = π((2+x)² - 2²) * 0.4
Set the volumes equal, as the earth taken out from the well forms the embankment:
V_well = V_embankment
176 = π((2+x)² - 2²) * 0.4
Solve for x:
This equation is a quadratic and can be solved using various methods. Here, we can expand the equation and simplify:
176 = π(4x² + 8x + 4 - 4)
176 = 4πx² + 8πx
44 = πx² + 2πx
Divide both sides by π:
14 ≈ x² + 2x
Factor the equation:
14 ≈ (x + 7)(x - 2)
Therefore, x ≈ 7 (neglecting the negative solution as it wouldn't make physical sense for the width).
Therefore, the width of the embankment is approximately 7 meters.
Answer:
Hence, on comparing the volume of well and the volume of embankment we can find the width of the embankment. Final solution: the width of the embankment when a well of diameter 4m is dug 14m deep. The earth taken out is spread evenly all around the well to form a 40cm high embankment is 7.48m.