An angriculture field is rectangular, with dimensions 100 m by 42 m. A 20 m deep well of diameter 14 m is dug in a corner of the field and the earth taken out is spread evenly over the remaining part of the field.Find the increase in the level of the field
The area of the field is 100m x 42m = 4200 square meters.
The area of the well is 1/4 x π x 14m x 14m = 153.94 square meters.
The volume of earth taken out to dig the well is 20m x 153.94 square meters = 3078.8 cubic meters.
The remaining area of the field is 4200 square meters - 153.94 square meters = 4046.06 square meters.
To find the increase in the level of the field, we need to divide the volume of earth taken out by the new area of the field:
3078.8 cubic meters / 4046.06 square meters = 0.761 meters (rounded to the nearest hundredth).
Therefore, the increase in the level of the field is 0.761 meters (or approximately 2.49 feet).
To find the increase in the level of the field, we need to determine the volume of earth that was taken out to create the well, and then calculate the area over which it was spread evenly.
Step 1: Calculate the volume of earth removed for the well:
The well is cylindrical in shape, so we can use the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height.
Given that the diameter of the well is 14 m, the radius (r) is half of that, which is 14/2 = 7 m.
The height (h) of the well is 20 m.
Calculating the volume, we have: V = π(7^2)(20) = 1540π m^3.
Step 2: Calculate the area of the rectangular field:
The area (A) of a rectangle is given by the formula A = length × width.
Given that the dimensions of the field are 100 m by 42 m, we can calculate the area: A = 100 × 42 = 4200 m^2.
Step 3: Determine the increase in the level of the field:
Since the earth removed from the well is spread evenly over the remaining part of the field, the increase in level is equal to the volume of earth removed divided by the area of the field.
Therefore, increase in level = Volume of earth removed / Area of field
Plugging in the values, we get:
increase in level = 1540π / 4200 m
So, the increase in the level of the field is 1540π / 4200 (approximately) or you can use a calculator to get the decimal value.