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Home » A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
CBSE | Class 10 | Exercise 13.3 | Maths | NCERT | Surface Areas And Volumes
A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

The state of the well will be tube shaped as given underneath.

Ncert solutions class 10 chapter 13-19

Given, Depth (h_1) of well = 14 m

Distance across of the roundabout finish of the well =3 m

Thus, Radius (r_1) = 3/2 m

Width of the bank = 4 m

From the figure, one might say that the bank will be a chamber having an external sweep (r_2) as

    \[\mathbf{4}+\left( \mathbf{3}/\mathbf{2} \right)\text{ }=\text{ }\mathbf{11}/\mathbf{2}\text{ }\mathbf{m}\]

and inward range (r_1) as 3/2m

Presently, let the tallness of bank be h_2

∴ Volume of soil burrowed from well = Volume of earth used to shape dike

    \[\mathbf{\pi }\times \mathbf{r_1^2}\times \mathbf{h}\text{ }=\text{ }\mathbf{\pi }\times \left( \mathbf{r_2^2}-\mathbf{r_1^2} \right)\text{ }\times \text{ }\mathbf{h_2}\]

Tackling this, we get, The tallness of the bank (h_2) as 1.125 m.

 

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