An agriculture field is rectangular with dimensions 100mby42m.a 20m deep well of diameter 14m isdugacorner of the field and earth out is spread evenly over the remaining part the field. Find the increase level of the field?
The area of the field is:
100m x 42m = 4200 sq.m
The area of the well is:
(π x 7²) / 4 x 20 = 1539.38 sq.m (divided by 4 since only a quarter of the circle is within the field)
So, the area of the remaining part of the field is:
4200 - 1539.38 = 2660.62 sq.m
When the earth from the well is spread over the remaining part of the field, the level of the field will increase by:
(1539.38 / 2660.62) x 20m = 11.61m (rounded to two decimal places)
Therefore, the increase in level of the field is 11.61m.
To find the increase in the level of the field, we need to first calculate the volume of the well and then divide it by the area of the field.
1. Calculate the volume of the well:
The well is cylindrical, so we can use the formula for the volume of a cylinder: V = πr^2h, where r is the radius of the well and h is the depth of the well.
Given that the diameter of the well is 14m, the radius will be half of that: r = 14m / 2 = 7m.
The depth of the well is given as 20m.
So, the volume of the well is V = π * (7m)^2 * 20m = 1540π m^3.
2. Calculate the area of the field:
The field is rectangular with dimensions 100m by 42m.
So, the area of the field is A = length * width = 100m * 42m = 4200 m^2.
3. Calculate the increase in level:
Since the earth dug out from the well is spread evenly over the remaining part of the field, the level of the field will be increased by the volume of the earth divided by the area of the field.
So, the increase in level is Δh = V / A = (1540π m^3) / (4200 m^2) ≈ 1.16 meters.
Therefore, the level of the field will increase by approximately 1.16 meters.