Question

(A well of diam. 4m is dug 14 m deeps the earth
the earth taken out is spread evently all around the well
to form a 40 cm high embankment. Find width
of embankment​

Answer 1

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■☆A well of diam. 4m is dug 14 m deeps the earth the earth taken out is spread evently all around the well to form a 40 cm high embankment. Find width of embankment☆■

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☆Let radius of embankment be = $\blue{r\: metre}$

$Radius\: of\: well(R)= \blue{2 m}$

$Depth(h) = \blue{14 m}$

$\boxed{\red{\bold{Volume \:of\: Well:}}}$

$\implies \pi R^2H$

$\implies \pi × 2^2 × 14$

$\implies \pi × 4 × 14$

$\blue{\implies 56 \pi m^3}$

$Radius\: of \: embankment = \purple{r \:m}$

$Height \: of\: embankment (h)= 40\:cm =\purple{ \displaystyle{\frac{40}{100}} m =\frac{2}{5}m}$

$\boxed{\red{\bold{Volume\:of\:embankment: }}}$

$\implies \pi r^2 h - \pi R^2 h$

$\implies \pi \left( r^2 × \displaystyle{\frac{2}{5}} - 2^2 × \frac{2}{5} \right)$

$\implies \pi \left( \displaystyle{\frac{2r^2}{5}} - \frac{8}{5} \right)$

$\purple{\implies \pi \left( \displaystyle{\frac{2r^2-8}{5}} \right)}$

$\boxed{\red{\bold{Equating\: the \: volumes:}}}$

$\implies \blue{56 \pi} = \purple{\pi \left( \displaystyle{\frac{2r^2 -8}{5}} \right)}$

$\implies 56 = \displaystyle{\frac{2r^2-8}{5}}$

$\implies 280 = 2r^2 - 8$

$\implies r^2 - 4 = 140$

$\implies r=\sqrt{144}$

$\green{\implies r = 12 m}$

$\boxed{\red{\bold{Width\:of \: embankment:}}}$

$\purple{r - R = 12m - 2m = 10m}$

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