Question

A well of diameter 2 m is dug 14 m deep. The earth taken out of it is spread evenly all around it to form and embankment of height 40 cm. Find the width of the embankment.

Answer 1

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➽A well of diameter 2 m is dug 14 m deep. The earth taken out of it is spread evenly all around it to form and embankment of height 40 cm. Find the width of the embankment.

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❀Let us suppose the shape of well is like as cylinder.

Diameter of well = 2 m

so, radius (r) = d/2 = 2/2 = 1 m

Height(h) of well = 14 m

❀Volume of right circular cylinder, V’ = πr²h

=π×1²×14.....................(1)

Given that,

length(l) of embankment= 40 cm

Let width of the embankment be x m

❀Volume of the embankment, V’’ = πr²h

= π ((1+x)2 – 1)2 x 0.4 ....................(2)

❀Since well is spread evenly to form the embankment,

so their volumes, V’ = V’’

➽ π × 14 = π ((1+x)2 – 1)2 x 0.4

➽ x = 5m

${\bf{\green{∴ Height\: of \:the\: embankment,\: x = 5cm}}}$

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Answer 2

Width of embankment = 5m

Step-by-step explanation:

Volume of the well = πr²h = 22/7 * 1 * 1 * 14 = 44 cu. m.

Radius of the quadrant = 3.5 m.

Let x be the width of the embankment.

Height of the embankment = 40cm = 0.4 m

Volume of the embankment = πr²h =  π ((1+x²) -1)² * 0.4

Both volumes are equal, so we get:

 π(1)(14) = π ((1+x²) -1)² * 0.4

 14/0.4 = (1+x²)² +1 -2(1+x)

   x = 5m

Width of embankment = 5m