# Thread: Mensuration - Volume and surface area

1. ## Mensuration - Volume and surface area

Question: A Well of diameter 3 Meter is dug 14 Meter deep. The earth taken out of it is spread evenly all around it in shape of circular ring of width 4 Meter to form an embarkment. Find the height of the embarkment.

2. Originally Posted by shaurya
Question: A Well of diameter 3 Meter is dug 14 Meter deep. The earth taken out of it is spread evenly all around it in shape of circular ring of width 4 Meter to form an embarkment. Find the height of the embarkment.

The volume of earth removed is

$v=\pi r^2h=\pi\left(\frac{3}{2}\right)^2(14)=\frac{63\pi }{2}$

The volume of the enbankment is

$V=\left(\frac{11}{2}\right)^2\pi h-\left( \frac{3}{2}\right)^2\pi h=28\pi h$

Now setting the volumes equal we can solve for h

$28 \pi h = \frac{63 \pi}{2} \iff h =\frac{63 \pi }{2} \cdot \frac{1}{28 \pi}=\frac{63}{56} m$

Okay I think I fixed it.

3. Hmm, your right but i cant figure out wat does it mnean by an embankment here. Can you give me a figuire or so? I couldnt understand the volume of embankment.

4. Originally Posted by shaurya
Hmm, your right but i cant figure out wat does it mnean by an embankment here. Can you give me a figuire or so? I couldnt understand the volume of embankment.
I've attached a rough sketch of the well and it's embankment.