Question

A plot of land in the form of rectangle has dimensions 250×160. A drain 10 m side in dug all around it and the earth dug out is evenly spread over the plot increasing its surface level by 40 cm. find the depth of the drain.

Answer 1

$\underline{\huge \mathfrak {{solution}}}$

$<b><i> let the depth of the drain be x metre$




Now width of the drain = 10 m

∴ volume of the drain = 2(270 × 10 × x)(160 × 10 × x)

= (5400 x + 3200 x) m³




The earth dug out from the drain let the spread over the plot, raising its height by 40 cm, i.e., 0.4 m.




∴ Volume if the earth spread on the plot = (250 × 160 × 0.4) m³ = 16000 m³



volume of drainlet = volume of earth spread on the rectangular plot



i.e., 8600 x = 16000 ⇒ x = 16000/8600




$\huge = 1.86 \: m.$



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Answer 2

Find the volume of the earth that was dug out:

250 x 160 x 0.4 = 16,000 m²

Find the area of the plot of land:

Area = 250 x 160 = 40,000 m²

Find the area of the plot of land and the drain:

Area = (250 + 10 + 10) x (160 + 10 + 10) = 48,600 m²

Find the area of the drain:

Area = 48600 - 40000 = 8600 m²

Define x:

Let x be the dept of the drain

Solve x:

8600x = 16000

x = 16000 ÷ 8600

x = 1.86 m

Answer: The dept of the drain is 1.86 m