Question

A well having 10 m inside diameter is dug 8.4m deep. earth is taken out of it and spread to a width of 7.5m to make embankment. find the height of the embankment.

Answer 1

A well having 10 m inside diameter is dug 8.4m deep. earth is taken out of it and spread to a width of 7.5m to make embankment.
To find the height of the embankment:

First find the volume of earth(soil) taken out
which is equal to the volume of Cylinder.

Well is on the form of Cylinder, inside diameter
10 m

Radius = 5m
deep/height = 8.4 m

Volume of soil taken out=
$\pi \: {r}^{2} h \: {m}^{3} \\ \\ = \frac{22}{7} \times 25 \times 8.4 \\ \\ = 22 \times 25 \times 1.2 \\ \\ = 660 \: {m}^{3}$

As embankment is to be made around the well.

Outside diameter = 10+7.5+7.5= 25 m

Outside radius = 12.5 m

Since ,earth taken out does not put inside the well,so we had to put the formula like

$\pi( {R}^{2} - {r}^{2})\:h = 660 \\ \\ \frac{22}{7} ( {(12.5)}^{2} - {(5)}^{2}) h = 660 \\ \\ h = \frac{660 \times 7}{22 \times (156.25-25)} \\\\h = \frac{660 \times 7}{22 \times (131.25)} \\\\ h = 1.6 \: m$

So, the height of the embankment will be 1.6 m.

Hope it helps.

Answer 2

Answer:

h=1.6 m . Hope this helps you