An agriculture field is in the form of a rectangle of length 20m width 14m . A 10m deep well of diameter 7m is dug in a corner of the field and the earth taken out of the well is spread evenly over the remaining part of the field. Find the rise in its level.
Answers
Given info : An agriculture field is in the form of a rectangle of length 20m width 14m . A 10m deep well of diameter 7m is dug in a corner of the field and the earth taken out of the well is spread evenly over the remaining part of the field.
To find : The rise in its level is ...
solution : area of rectangular field = length × width
= 20 m × 14 m
= 280 m²
area of circular part of the field = π(7/2 m)²
= 22/7 × 7/2 × 7/2
= 11 × 3.5
= 38.5 m²
so, remaining area of field where we have to spread the earth = area of rectangular field - area of circular part of the field
= 280 m² - 38.5 m²
= 241.5 m²
let the rise in the level of field is h.
volume of the earth taken out from the well = volume of remaining part of the field
⇒π(7/2 m)² × 10 m = 241.5 m² × h
⇒22/7 × 7/2 × 7/2 × 10 = 241.5 × h
⇒h = 385/241.5 = 1.594 m
Therefore the rise in the level of remaining part of the field is 1.594 m
Given : A house plot is the form of rectangle of length 20m and width 14m. A 10 m deep well of diameter of 7 m m is dug in a North East corner of the in a northeast corner of the plot and earth Taken out of the well played evenly over the remaining part of the field
To Find : the volume of the earth dug
Height of Earth spread on remaining field
Solution:
Well Diamter = 7 m
Radius r = 7/2 m
Depth = 10 m
Volume = πr²h
= (22/7)(7/2)² * 10
= 11 * 7 * 5
= 385 m³
Plot area = 20 * 14 = 280 m²
remaining area = plot area - well area
well area = πr² = (22/7) (7/2)² = 77/2 = 38.5 m²
remaining area = 280 - 38.5 = 241.5 m²
height increase in remaining area = h
Hence 241.5 * h = Volume of earth dug
=> 241.5 * h = 385
=> h = 1.594 m
Height of level = 1.594 m
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