Question

A well of diameter 14 m. is dug 15 m. deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 7 m. to form an embankment. Find the height of the embankment.

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

Volume of the earth taken out of the well = 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

Area of embankment = 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 ANSWER WILL HELP YOU..

Answer 2

Dear Student,

Answer:Height of embankment is 5 m

Solution: well shape is like cylinder.

The amount of earth/soil taken out is equal to the volume of the cylinder.

Volume of cylinder =
$\pi \times {r}^{2} \times h$
here Diameter is 14 m
So,radius is 7 m

h= 15 m

Volume of earth taken out =
$= 3.14 \times ( {7)}^{2} \times 15 \\ = 2307.9 \: {m}^{3}$
This amount of earth spread around the well,
thus volume of earth taken out is equal to that spread around the well

$2307.9 = \pi \times ( {14}^{2} - {7}^{2}) \times h \\ h = \frac{2307.9}{147 \times \pi } \\ h = 5m$
hope It helps you