A 40m deep well with radius 3.5m is dug and the earth taken out is evenly spread to form a platform of dimensions 28m by 22m.find the hight of the platform.
To find the height of the platform formed by the earth taken out of the well, we need to calculate the volume of the well and the area of the platform.
First, let's find the volume of the well using the formula for the volume of a cylinder:
Volume of a cylinder = π * r^2 * h
In this case, the radius (r) is given as 3.5m, and the height (h) is given as 40m.
Volume of the well = π * (3.5)^2 * 40
Next, let's find the area of the platform. The platform is in the shape of a rectangle, so the area can be calculated using the formula:
Area of a rectangle = length * width
In this case, the length is given as 28m, and the width is given as 22m.
Area of the platform = 28 * 22
Now, the earth taken out from the well is evenly spread to form the platform. This means that the volume of the well should be equal to the volume of the platform. In other words:
Volume of the well = Area of the platform * height of the platform
Using this equation, we can solve for the height of the platform:
π * (3.5)^2 * 40 = 28 * 22 * height of the platform
Simplifying the equation:
(3.5)^2 * 40 = 28 * 22 * height of the platform
Solving for the height of the platform:
height of the platform = (3.5)^2 * 40 / (28 * 22)
Now, calculate the value:
height of the platform = 3.5^2 * 40 / (28 * 22)
Using a calculator, we get:
height of the platform ≈ 4.31 m
Therefore, the height of the platform formed by the earth taken out of the well is approximately 4.31 meters.