Question

a well 10m inside diameter is dug 14m deep earth taken out of it is speed all arond to a width of 5m to form an embankment find its height

Answer 1

Given that internal diameter of the well = 10m.

Then the internal radius of the well r1 = d/2 

                                                               = 10/2

                                                               = 5m.


Given that depth of the well h1 = 14m.

Volume of the earth dug out from the well = pir^2h1

                                                                       = 22/7 * 5^2 * 14

                                                                       = 22 * 25 * 2

                                                                       = 1100.   -------- (1)


Then the external radius of the embarkment r2 = (5 + 5)

                                                                                = 10m.


Volume of the earth in the embarkment = pih(r2^2 - r1^2)

                                                                    = 22/7 * h * (10^2 - 5^2)

                                                                    = 22/7 * h * 100 - 25

                                                                    = 1650h/7   ------ (2)


On solving (1) & (2), we get

1100 = 1650h/7

1650h = 7700

h = 7700/1650

h = 14/3

h = 4.66m.


Therefore the height = 4.66 m.


Hope this helps!

Answer 2

internal diameter of the well = 10m.

Then the internal radius of the well r1 = d
___
2

= 10/2

= 5m.


depth of the well h1 = 14m.

Volume of the earth dug out from the well =
$2\pi \: r \: = \frac{22}{7} \times 5 {}^{2} \times 14 = 1100$




external radius of the embarkment r2 = (5 + 5)

=10m.


Volume of the earth in the embarkment =
$2\pi \: r \: = \frac{22}{7} \times h \: \times 10 {}^{2} - 5 {}^{2} \\ = h \: \times 100 - 25 \\ = h \: \: = 1650$


we get

1100 = 1650h/7

1650h = 7700

h = 7700/1650

h = 14/3

h = 4.66m.


Therefore the height = 4.66 m.