Question

32. A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is spread
all around it to a width of 7.5 m to form an embankment. Find the height of the
embankment.​

Answer 1

Answer:

h= 1.6m

Step-by-step explanation:

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 10m

Radius = 5m

deep/height = 8.4 m

Volume of soil taken out

=πr² hm³

=

$\frac{22}{7} \times 25 \times 8.4$

= 22 x 25 x 1.2

= 660 m³

As embankment is to be made around the well.

Outside diameter = 10+7.5+7.5=25m

Outside radius = 12.5m

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

π(R^2 - r^2) h = 660

22/7 * ((12.5) ^ 2 - (5) ^ 2) * h = 660

h =

$= \frac{660 \times 7}{22 \times (156.25 - 25}$

$= \frac{660 \times 7}{22 \times 131.25}$

h = 1.6m

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

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