A field is 150 m long and 70 m broad. a circular tank of radius 5.6 m and depth 20 cm is dug in the field and the earth taken out of it is spread evenly over the field. find the height of the field raised by it.
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volume of circular tank dug is π*r^2*h
where r = 5.6m ; h = 20 cm = 0.2m
volume = π*(5.6)^2*0.2
volume of tank = 19.7 m^3
area of field = 150 * 70 = 10500 m^2
as earth taken out of it is spread evenly over the field
area of circular tank = π*r^2 (as earth is not put over the area of tank)
= 98.52 m^2
thus
total area to put earth over it = area of field - area of tank
10500-98.52 =10401.5 m^2
thus volume of field = area * h (as field is now a cuboid)
area is constant as earth is spread evenly over the field
thus volume of tank = thus volume of field
or
19.7 = 10401.5 * h
or h = 19.7/10401.5
h = 0.001894 m
or h = 0.1894 cm
or the height of the field raised by it is 0.1894 cm
where r = 5.6m ; h = 20 cm = 0.2m
volume = π*(5.6)^2*0.2
volume of tank = 19.7 m^3
area of field = 150 * 70 = 10500 m^2
as earth taken out of it is spread evenly over the field
area of circular tank = π*r^2 (as earth is not put over the area of tank)
= 98.52 m^2
thus
total area to put earth over it = area of field - area of tank
10500-98.52 =10401.5 m^2
thus volume of field = area * h (as field is now a cuboid)
area is constant as earth is spread evenly over the field
thus volume of tank = thus volume of field
or
19.7 = 10401.5 * h
or h = 19.7/10401.5
h = 0.001894 m
or h = 0.1894 cm
or the height of the field raised by it is 0.1894 cm
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