The well is dug 14m deep. Its radius is 2m. The earth dug out is evenly spread out on a rectangular field of dimensions 10m*4m. Find the height of the platform raised.
To find the height of the platform raised, we need to calculate the volume of the earth dug out from the well and then divide it by the area of the rectangular field.
First, let's calculate the volume of the earth dug out from the well. The well can be represented as a cylinder, where the radius (r) is 2m and the height (h) is 14m. The formula for the volume of a cylinder is:
Volume = π * r^2 * h
Substituting the values, we have:
Volume = π * 2^2 * 14
Volume = π * 4 * 14
Volume = π * 56
Next, let's calculate the area of the rectangular field. The dimensions are given as 10m*4m, so the area can be found by multiplying the length (10m) by the width (4m):
Area = Length * Width
Area = 10 * 4
Area = 40
Now, to find the height of the platform raised, we divide the volume of the earth dug out by the area of the rectangular field:
Height of platform raised = Volume / Area
Height of platform raised = (π * 56) / 40
To get an exact numerical value, we can use the approximation π = 3.14:
Height of platform raised ≈ (3.14 * 56) / 40
Height of platform raised ≈ 1.57
Therefore, the height of the platform raised is approximately 1.57 meters.
what platform?
volume = area * height = 40h
the well's volume is pi r^2 h = 56pi
so, 40h = 56pi