Question

A well of inner diameter 14 m is dug to a depth of 12 m. Earth taken out of it has been evenly spread all around it to a width of 7m to form an embankment.
Find the height of the embankment so formed.​

Answer 1

$\huge\star{\green{\underline{\mathfrak{Answer :-}}}}$

$\bf{Given}\begin{cases}\sf{The\:inner\:diameter\:of\:the\:well=14\:m}\\\sf{Depth\:of\:the\:well=12\:m}\\\sf{Width\:of\:embankment=7\:m}\end{cases}$

$\bf{To\:Find:-}$

• The height of the embankment

$\bf{Solution:- }$

Volume of cylinder is:-

$\huge{\boxed{\tt{\pi {r}^{2}h}}}$

$\leadsto\tt{\dfrac{22}{7}\times{(7)}^{2}\times12}$

$\huge\leadsto{\boxed{\tt{1848\:{cm}^{3}}}}$

As we know the earth taken out is spreaded evenly around the well as an embankment.

So, The volume of the earth taken out = The volume of the embankment.

Here, we will use the formula to find the volume of hollow cylinder.

The formula is:-

$\huge{\boxed{\tt{\pi({r_1}^{2}-{r_2}^{2})h, r_1 > r_2}}}$

The outer radius = The inner radius + width.

So, the outer radius is 14 cm.

$\leadsto\tt{\dfrac{22}{7}\times({14}^{2}-{7}^{2})\times h = 1848}$

$\leadsto\tt{\dfrac{22}{7}\times (196-49) \times h = 1848}$

$\leadsto\tt{\dfrac{22}{7}\times 147 \times h = 1848}$

$\leadsto\tt{462 \times h = 1848}$

$\leadsto\tt{h = \dfrac{1848}{462}}$

$\huge\leadsto{\boxed{\red{\tt{4\:m}}}}$

$\rule{200}4$

Answer 2

$\huge{ \fbox{ \fbox { \bigstar{ \mathfrak { \blue{answer}}}}}}$

HERE INNER DIAMETER = 14 m

=> r =14 \2 = 7m

Volume of earth dug out = ( 22 \7 × 7×7× 12 )

=> 1848 m^3

WIDTH OF EMBANKMENT = 7m

TOTAL RADIUS = [ 7 + 7] = 14m

VOLUME OF EMBANKMENT = TOTAL VOLUME - INNER VOLUME

=> 22\7 ×h [ 14 ^2 - 7 ^2 ]

=> 462h m^3

=> 462h = 1848

=> h = 1848 \ 462 = 4

SO THE HEIGHT OF THE EMBANKMENT FORMED IS =

$\huge { \fbox{ \mathfrak { \green{4m}}}}$

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