Question

# A well of diameter $4m$ is dug $21m$ deep. the earth taken out of its has been spread evenly all around it in the shape of a circular ring of width $3m$ to form an embankment. Find the height of the embankment.

Open in App
Solution

## Step 1: Find the volume of the well dug. Given that, Diameter $=4m$Radius $=2m$Height $=21m$The volume of soil dug from the well $={\mathrm{\pi r}}^{2}\mathrm{h}$ $=\pi ×2×2×21\phantom{\rule{0ex}{0ex}}=84\pi$Step 2: Find the height of the embankment. The volume of soil dug from the well $=$ The volume of earth used to form the embankment $⇒84\pi =\pi ×\left({5}^{2}-{2}^{2}\right)×h\phantom{\rule{0ex}{0ex}}\therefore h=\frac{84}{25-4}\phantom{\rule{0ex}{0ex}}h=\frac{84}{21}\phantom{\rule{0ex}{0ex}}h=4m$Hence, the height of the embankment is $4m.$

Suggest Corrections
3
Related Videos
MATHEMATICS
Watch in App
Explore more