Question

A well of inner diameter 14m is dug to a depth of 15m,mud taken out of it has been evenly spread all around into a width of 7m to form an embankment .find the height of the embankment so formed.

Answer 1

Here, a well is dug and Earth taken out of it is used to form an embankment.

Given:

Inner Diameter of the well= 14 m

Inner Radius of the well (r) = 14/2 m = 7 m

Height of the well(h) = 15 m

Volume of the earth taken out of the well = πr²h

= 22/ 7 ×(7)²×15

= 22× 7×15= 2310 m³

Width= 7m

Outer radius of the embankment R =inner radius + width

Outer radius (R)= 7 + 7 = 14m

The embankment is in the form of cylindrical shell, so area of embankment


Area of embankment = outer area - inner area

= πR² - πr² = π(R²-r²)

= (22/7) ( 14² - 7²)

= 22/7(196-49)

= 22/7 × 147

= 22 × 21

= 462 m²


Volume of embankment= volume of earth taken out on digging the well

Area of embankment × height of embankment= volume of earth dug out

Height of embankment= volume of earth dug out/area of the embankment

Height of the embankment = 2310 / 462

Height of embankment= 5 m

Hence, the height of the embankment so formed is 5 m ==================================================================
Hope this will help you.....

Answer 2

Solution :-

Both well and the embankment are in the shape of cylinder.

Since the mud is evenly spread all around the well to form the embankment, then the volume of well = volume of embankment

Volume of well = πr²h

Diameter = 14 m
then radius = 14/2 = 7 m
Height = 15 m

⇒ π*7*7*15 

⇒ Volume of well = 735 π m³

Volume of the embankment -

The embankment is in the shape of a hollow cylinder.

It inner diameter =  14 m

So, Radius r = 14/2 = 7 m

Its outer radius R = inner radius + width

⇒ 7 + 7 = 14 m

Volume of inner part of the cylinder = πr²h

⇒ π(7)²*h

= 49 πh m³

Volume of the outer part of the cylinder = πR²h

⇒ π(14)²*h

⇒ 196 πh m³


Volume of embankment = Volume of outer part - Volume of inner part

⇒ 196 πh m³ - 49 πh m³

Volume of embankment = 147 πh m³

Now,

Volume of well = Volume of embankment

735 π m³ = 147 πh m³

⇒ h = 735/147

⇒ h = 5

So, the height of the embankment is 5 m

Answer.