Question

a well of diameter 3m is dug 14m deep the earth taken out of it has been spread evenly allvaround it in the shape of a circular ring of width 4m to form a plateform .find the height of the plateform.(take r=22÷7)​

Answer 1

Given:

→ The diameter of well is 3m

So, radius (R) of the well = 3/2 = 1.5 m

→ The height (H) of the well (as dug deep) is 14m

• The earth(i.e soil) is taken out and spread eventually all around the shape of a circular ring.

→ Width of the ring is 4m

To find:

The height of the circular ring.

So,

The volume of the well is equal to the volume of the circular ring.

As the soil is dug from well and put around it to make a platform of a circular ring.

Thus,

$\boxed{\boxed{\bf \pi R^{2}H = \pi h [(r_{2})^{2}- (r_{1})^{2}]}}$

In both, the sides π will get cancelled.

$\implies R^{2}H = h [(r_{2})^{2}- (r_{1})^{2} ]$

Putting the respective values.

$\implies (1.5)^{2}*14 = h [(5.5)^{2}- (1.5)^{2}]$

$\implies 2.25*14 = h * [30.25 - 2.25]$

$\implies 31.5 = h * [28]$

By transporting 28 to LHS we get,

$\implies \frac{31.5}{28} = h$

$\therefore h = 1.125m$

Hence,

• The height of the circular ring (plateform) is = h = 1.125m