Question

a well diameter of 14 M is dug 15 deep the earth taken out it has been spread evenly all around it in the shape of circular ring of which 7 to form an embankment find the height of embankment​

Answer 1

Answer:-

Height of embankment is 5 m

Step - by - step explanation:-

Given that :-

Let, h metre be the height and r metre be the radius of well.

h= 15 m , radius (r) = d/2 = 7 m

• Volume of the earth dug out (v)

$\implies \: \bf{ v = \pi \: {r}^{2} h} \\ \\ \implies \: \bf{v \: = \frac{22}{7} \times 7 \times 7 \times 15} \\ \\ \implies \: \bf{v \: = 22 \times 7 \times 15} \\ \\ \implies \: \bf{ v = 2310 \: {m}^{3} }$

Let ,

• k be the height of embankment.

The shape of embankment will be like as the shape of cylinder of internal radius

R = 7 m and external radius S= 14 m .

• Now the volume of embankment (u)

$\implies \bf{ \:u = \pi \big( {s}^{2} - {r}^{2} \big) \times k} \\ \\ \implies \: \bf{u = \pi \big( {(14)}^{2} - {(7)}^{2} \big) \times k} \\ \\ \bf{ \implies \:u = \pi(196 - 49) \times k} \\ \\ \implies \: \bf{u \: = \pi \times 147 \times k}$

Now ,Volumes be equal (v =u)

$\implies \: \bf{\pi \times 147 \times k = 2310} \\ \\ \implies \: \bf{k \: = \frac{2310 \times 7}{22 \times 147} } \\ \\ \implies \: \boxed{\bf{k \: = 5m}}$