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प्रश्न
A well with 6 m diameter is dug. The earth taken out of it is spread uniformly all around it to a width of 2 m to form an embankment of height 2.25 m. Find the depth of the well.
उत्तर
Radius of the well (r)
= `(6)/(2)`
= 3m
Volume of earth dug out of the well
= πr2h ...(Volume of cylinder)
= π x (3)2 x h
= 9πh m2
Area of embankment = πR2 - πr2
Where R = r + width of the embankment
= 3 + 2
R = 5m
Area of embankment
= π52 -π32
= 16π m2
Volume of earth dug out for the embankment
= area of embankment x height
9πh = 16π x 2.25
h = `(16π xx 2.25)/(9π)`
∴ h = 4m
∴ The depth of the well is 4m.
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