A well of diameter 7cm is dug 22.5m deep.The earth taken out it is spread evently all around it to a width of 10.5 to from an embankment .find the height of the embankment.
To find the height of the embankment, we need to understand the dimensions and geometry of the situation.
1. Diameter of the well: 7 cm
2. Depth of the well: 22.5 m
3. Width of the embankment: 10.5 m
First, let's find the volume of the well, as it will help us determine the volume of the embankment.
The volume of a cylinder (well) can be calculated using the formula:
V = πr^2h
where V is the volume, π is approximately 3.14, r is the radius, and h is the height.
Given that the diameter is 7 cm, the radius (r) of the well is half of the diameter, which is 3.5 cm or 0.035 m (converted to meters).
Calculating the volume of the well:
V_well = π × (0.035)^2 × 22.5
= 3.14 × 0.035^2 × 22.5
≈ 0.277 m^3
Since the earth taken out from the well is spread evenly to form an embankment around it, the volume of the embankment will be equal to the volume of the earth removed.
Now, let's find the volume of the embankment:
V_embankment = V_well
= 0.277 m^3
To find the height of the embankment, we need to know the area of the base. In this case, the base of the embankment is a circle with a radius equal to the well radius plus the embankment width.
Calculating the radius of the embankment:
R_embankment = r_well + width
= 0.035 m + 10.5 m
= 10.535 m
To find the area of the base, we use the formula for the area of a circle:
A_base = πR_embankment^2
= 3.14 × (10.535)^2
≈ 348.59 m^2
Now we have the volume and the base area of the embankment. To find the height of the embankment, we'll divide the volume by the base area:
Height_embankment = V_embankment / A_base
= 0.277 / 348.59
≈ 0.000794 m
Therefore, the height of the embankment is approximately 0.000794 meters, or about 0.794 millimeters.
that's some skinny well!
v = pi r^2 h = pi(3.5)^2 (2250) = 86590 cm^3
If the embankment is 10.5 cm wide, starting at the edge of the well (complete description of the problem is important!)
86590 = pi (17.5^2 - 7^2)h
so, h = 107 cm