Question

In a village, a well with 10 m inside diameter, is dug 14 m deep. Earth taken out of it is spread all around to a width of 5 m to form an embankment. Find the height of the embankment. What value of the villagers is reflected here?

Answer 1

Given: diameter of the well (d) = 10 m

$Radiusofthewell\left(l\right)=\frac{d}{2}=\frac{10}{2}=5m$

and Depth of well (h) = 14 m

$Volumeofearthdugout=\pi \times r^2\times h$

$=\pi \times 5^2\times 14m^3$

$=350\pi m^3$

Let the height of embankment be H m.

$Nowvolumeofembankment=350\pi \times m^3$

$\Rightarrow \pi (r+5{)}^2\times H–\pi \times r^{2}H=350\times pi$

$\Rightarrow H\times \left[\right(5+5{)}^2–5^2]=350$

⇒ H (100 – 25) = 350

⇒ H = $\frac{350}{75}=\frac{14}{3}=4.66$

Hence the height of the embankment is 4.66 m.