Question

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

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Solution

## Find the height of the embankmentDepth $\left({h}_{1}\right)$ of well $=14m$The radius $\left({r}_{1}\right)$ of the circular end of the well $=\frac{3}{2}m$Width of embankment $=4m$It can be observed that our embankment will be cylindrical having an outer radius, $\left({r}_{2}\right)=4+\frac{3}{2}=\frac{11}{2}m$Let the height of the embankment be $\left({h}_{2}\right)$The volume of soil dug from the well $=$Volume of earth used to form the embankment $\pi ×{{r}_{1}}^{2}×{h}_{1}=\pi ×\left({{r}_{2}}^{2}-{{r}_{1}}^{2}\right)×{h}_{2}\phantom{\rule{0ex}{0ex}}\pi ×{\left(\frac{3}{2}\right)}^{2}×14=\pi ×\left[{\left(\frac{11}{2}\right)}^{2}–{\left(\frac{3}{2}\right)}^{2}\right]×{h}_{2}\phantom{\rule{0ex}{0ex}}\therefore {h}_{2}=\frac{9}{8}\phantom{\rule{0ex}{0ex}}=1.125m$So, the height of the embankment will be $1.125m.$

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