Question

A well with diameter 14 m is dug 8 m deep. The earth taken out of it has been evenly
spread all around it to a width of 21m to form an embankment. Find the height of embankment.​

Answer 1

Answer:

this is your answer.hope it is correct.

Answer 2

${\huge{\underline{\underline{\bf{Question:-}}}}}$

Q) A well with diameter 14m is dug 8m deep . The earth taken out of it has been evenly spread all around it to a width of 21m to form an embankment. Find the height of embankment .

${\huge{\underline{\underline{\rm{Answer\checkmark}}}}}$

$\frak{Given}\begin{cases}\rm{Diameter\:of\:well=\bf{14\:m}}\\\rm{Depth\:of\:well=\bf{8m}}\\\rm{The\:earth\:taken\:out\:of\:it\:has\:been\:evenly\:spread\:to\:form\:an\:\bf{embankment}}\\\rm{Width\:of\:embankment=\bf{21\:m}}\end{cases}$

${\underline{\underline{\frak{\dag\:\:To\:Find:}}}}$

• The height of the embankment .

${\underline{\underline{\frak{\dag\:\:Required\:Solution:}}}}$

• In this question, we would first find the volume of eath taken out of the well.

• Since we are making an embankment , so, the volume of the earth taken out of the well would be equal to the volume of the embankment.

• The shape of the embankment is like a hollow cylinder.

$\bull \sf \: volume \: of \: cylinder= \pi {r}^{2} h$

$\sf\bull\:volume\:of\:hollow\:cylinder=\pi(R^2-r^2) H$

Refer to the attachment ,

In the attachment,

• Green Part = Embankment.
• Orange Part = Well.

Here ,

• r (radius of well ) = $\sf\dfrac{14}{2}=7\:m$
• h ( depth of well ) = 8 m
• R ( radius of embankment + well ) = 21 + 7 m = 28 m.
• H = Height of embankment.

$\rightarrow\sf\:Volume\:of\:well=Volume\:of\:embankment\\\\\sf\colon\implies\:\cancel{\pi}r^2\times h = \cancel{\pi}(R^2-r^2) H\\\\\sf\colon\implies\: 7^2\times8=(28^2-7^2) H\\\\\sf\colon\implies\:49\times8=(784-49) H \\\\\sf\colon\implies\: \cancel{49}\times8=\cancel{735}\times H\\\\\sf\colon\implies\: 8=15\times H\\\\\colon\implies\: \underline{\boxed{\tt{\pink{H=\bf\dfrac{8}{15}\: m }}}}$

So,

The height of the embankment would be $\bf\dfrac{8}{15}\:m$ or 0.5333 m or 53.33 cm .

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