This is one of the important question from the cbse board exam point of view because in 2014 cbse board exam this question was asked. Question number 31 from RS Aggarwal book page number 812, exercise 17B, chapter volume and surface area of solid.
In a village, a well with 10 m inside diameter, is dug 14 m deep. Earth taken out of it is spread all around to a width 5 m to form an embankment. Find the height of the embankment. What value of the villagers is reflected here?
Radius of well, R = 10/2 = 5 m,
Depth of the well, H = 14 m
Width of the embankment = 5 m,
the outer radius of the embankment, r = R+5 = 5 +5 = 10 m
the inner radius of the embankment R = 5 m
Height of the embankment = H
volume of the embankment = volume of the well
[πr² – πR²]H = πr²h
π [r² – R²] H = πr²h
[r² – R²] H = r²h
[10² – 5²] H = 5² * 14
H = [5² * 14] / [100 – 25]
H= 14/3 m
∴ the height of the embankment H is 14/3 m