A well with 10m inside diametre is dug 14m deep Earth taken out of it is spread all around - Maths - Surface Areas and Volumes

Question

A well with 10m inside diametre is dug 14m deep Earth taken out
of it is spread all around to a width of 5m to form an embankment
Find the heigh of the embankment

Priyanka Kedia · Accepted Answer

Given, Diametre of well = 10 m

So, Radius of well (r) = 10/2 = 5 m

And, depth of well (h) = 14 m

$Q u a n t i t y o f e a r t h t a k e n o u t = V o l u m e o f t h e w e l l = π r^{2} h = \frac{22}{7} \times {(5)}^{2} \times 14 = 1100 m^{3}$

Given, width of embankment = 5 m

Let height of embankment = h m

Its internal radius (r) = 5 m and external radius (R) = 5 + 5 = 10 m

The embankment is in the form of hollow cylinder. So,

$V o l u m e o f e m b a n k m e n t = π (R^{2} - r^{2}) h = \frac{22}{7} \times ({(10)}^{2} - 5^{2}) \times h = \frac{22}{7} \times 75 \times h m^{3}$

Since, earth taken out of its spread all around to a width of 5 m to form an embankment. Therefore,

$V o l u m e o f e m b a n k m e n t = V o l u m e o f w e l l \frac{22}{7} \times 75 \times h m^{3} = 1100 m^{3} h = \frac{1100 \times 7}{22 \times 75} = 4.67 m$

Hence, height of the embankment is 4.67 m.

A well with 10m inside diametre is dug 14m deep. Earth taken out of it is spread all around to a width of 5m to form an embankment. Find the heigh of the embankment.