A 40 m deep well with radius 3.5 m is dug and the earth taken out is evenly spread to form a platform of dimension 28 m by 22 m. find the height of the platform
To find the height of the platform, we need to first calculate the volume of earth taken out from the well and then use it to determine the height.
1. Calculating the volume of the well:
The well is in the shape of a cylinder, so we can use the formula for the volume of a cylinder: V = πr^2h.
Given: radius (r) = 3.5 m, depth (h) = 40 m.
Therefore, the volume of the well = π * (3.5^2) * 40 cubic meters.
2. Calculating the volume of the platform:
The platform is a rectangular shape, so we can use the formula for the volume of a rectangular prism: V = lwh.
Given: length (l) = 28 m, width (w) = 22 m.
Therefore, the volume of the platform = 28 * 22 * H cubic meters (where H is the height).
3. Equating the volumes of the well and the platform:
Since the earth taken out from the well is evenly spread to form the platform, the volumes should be equal.
So, we have: π * (3.5^2) * 40 = 28 * 22 * H.
4. Solving for the height (H):
Rearranging the equation, we get: H = (π * (3.5^2) * 40) / (28 * 22).
Calculate the right side of the equation to find the height H.
By following these steps, you can find the height of the platform.
To find the height of the platform formed by the earth taken out from the well, we need to calculate the volume of the earth dug out and then divide it by the area of the platform.
First, let's calculate the volume of the well. The well can be represented as a cylinder, so we can use the formula for the volume of a cylinder:
V_well = π * r^2 * h
where V_well is the volume of the well, r is the radius, and h is the height. Substituting the given values:
V_well = π * (3.5m)^2 * 40m
= 1540π m^3
Next, let's calculate the area of the platform. The platform has the shape of a rectangle, so we can use the formula for the area of a rectangle:
A_platform = length * width
where A_platform is the area of the platform. Substituting the given values:
A_platform = 28m * 22m
= 616m^2
Finally, we can find the height of the platform by dividing the volume of the well by the area of the platform:
height = V_well / A_platform
= (1540π m^3) / (616m^2)
≈ 7.93m
Therefore, the height of the platform formed by the earth taken out from the well is approximately 7.93 meters.
the volume of the well is ... π r^2 h ... π * 3.5^2 * 40
the volume of the platform is ... L * W * H ...28 * 22 * H