Question

a well having 10m inside diameter is dug 8.4m deep.earth is taken out and spread all around it to a width of 7m to form a beautiful embankment.find the height of the embankment.the contractor charged rs 500 per cube meter for digging and making the circular embankment .he measured the height of the embankment as 2m.how much extra money he made?

Answer 1

.Radius of well,r=5m
and,it's depth=8.4m
so, volume of earth dug out=pi×r^2×h
=22/7×5×5×8.4
=550/7×8.4
=660m^3.
Width of embankment=7m
external radius =7+5=12m
internal radius =5m.
Area of embankment =
pi×[(12^2)-5^2]m^2
=22/7×(144-25)m^2
=(22/7×119)m^2
=374m^2.
therefore height =(660/374)m
=1.76471 m. now,
volume of embankment =pi×h×(R^2-r^2)
=22/7×1.76471×(12^2-5^2)
=5.54623×(144-25)
=5.54623×119
=660.00137 m^3
now, since the contractor has taken height as 2m therefore volume=pi×h×(R^2-r^2)
=22/7×2×(12^2-5^2)
=44/7×119
=44×17=748 m^3.
Now, cost per m^3=500
therefore cost of 660.00137 m^3=
660.00137×500=330000.685
Also, cost of 748 m^3=748×500=374000.
Therefore extra money made by him=374000-330000.685=Rs 43999.315