Question

A well having 3.5 m diameter and 20m deep is to be dug in a rectangular field 20m by 14m. The earth taken out it has been spread evenly all-round the well to the width of 2m, to form an embankment, find the height of the embankment.

Answer 1

I am not sure about the answer

Answer 2

Answer:

Height of embankment is 5.57 cm

Step-by-step explanation:

Given: Diameter of Well = 3.5 m

           Depth of well = 20 m

           Width of Embankment = 2 m

To find: Height of Embakmnet

Well in shape of cylinder, so

Diameter = 3.5 m

⇒ r $=\frac{3.5}{2}$ cm

height, h =20 m

Volume of earth taken out from well = volume of cylinder

                                                             = $\pi r^2h$

                                                             = $\frac{22}{7}\times(\frac{3.5}{2})^2\times20$

                                                             = $\frac{22}{7}\times\frac{35}{20}\times\frac{35}{20}\times20$

                                                             = $\frac{11\times35}{2}$

                                                             = $192.5\:\:cm^3$

Embankment is in shape of Cylinder.

Let height of embankment be $h_1$

Radius of Outer cylinder of embankment, R = r + 2 = $\frac{3.5}{2}+2$

R =  $\frac{7.5}{2}$

Now volume of embankment = volume of outer cylinder of embankment -  

                                                    volume of inner cylinder i.e., well

                                                 = $\pi R^2h_1-\pi r^2h_1$

                                                 = $\pi h_1(R^2-r^2)$

                                                 = $\pi h_1((\frac{7.5}{2})^2-(\frac{3.5}{2})^2)$

                                                 = $\frac{22}{7}\times h_1\times(\frac{44}{4})$

                                                 = $\frac{242}{7}\times h_1\:cm^3$

Volume of embankment = Volume of earth taken out

$\frac{242}{7}\times h_1\:\:=\:\:192.5$

$h_1\:\:=\:\:\frac{1925}{10}\times\frac{7}{242}$

$h_1\:\:=\:\:5.57\,cm$

Therefore, Height of embankment is 5.57 cm.