Question

A well of diameter 3 m and 14 m deep is dug. The earth taken out of it has been evenly spread all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment

Answer 1

$\huge{\bf{\underline{\overline{\mathfrak{\red{Solution:-}\mid}}}}}$

Here,

Depth of the well, h = 14m

Radius of the well, r = $\bf \frac{3}{2}m$ = 1.5m

Radius of the embankment, h' = 4m

So, outer radius, R = (1.5+4) = 5.5m

Height of the embankment, h' = ?

Now,

A/Q

Volume of embankment = Volume of cylinder

$\implies\tt \pi {R}^{2} h' - \pi {r}^{2} h' = \pi {r}^{2}h$

$\implies\tt {R}^{2} h' - {r}^{2} h' ={r}^{2} h$

$\implies\tt h'( {R}^{2} - {r)}^{2} = {(1.5)}^{2} \times 14$

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

$\implies\tt h'(5.5 + 1.5)(5.5 - 1.5) = 2.25 \times 14$

$\implies\tt h' \times 7 \times 4 = 2.25 \times 14$

$\implies\tt h' = \frac{2.25 \times 14}{7 \times 4}$

$\implies\tt h' = \frac{2.25}{2}$

$\implies\tt h' = 1.125 \: m$

Thus, height of the embankment is 1.125 m