Question

a well of diameter 3m is dug 21m deep. the earth taken out if its spread evenly all around it to width of 4m to form an embankment. find the height of the embankment.

Answer 1

Answer:

the height  of the embankment is 0.5235 m.

Step-by-step explanation:

Diameter of well = 3 m

Radius of well = $\frac{Diameter}{2}$ = 1.5 m

Depth of well = 21 m

Well is in the shape of cylinder  

Volume of well = $\pi r^{2} h$

                 = $\pi( 1.5^{2}) 21$

                  =148.365 m³

Radius of embankment = Radius of well + width

                                            = 1.5 + 8

                                            = 9.5 m

Since , Embankment is in the shape of cylinder .  

So, volume of embankment =  $\pi r^{2} h$

                                             = $\pi (9.5^{2}) h$

                                            = 283.385h

Since the earth is taken out from the well is used to make embankment .

So, volume will be equal.

148.365 =283.385h

h = $\frac{148.365}{283.385}$

h = 0.5235 m    

Hence the height  of the embankment is 0.5235 m.