a pit is dug in the shape of a cuboid with dimensions 10m*8m*3m. the earth taken out is spread evenly on a rectangular plot of land with dimensions 40m*30m. what is the increase in the level of the plot.
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To find the increase in the level of the plot, we need to calculate the volume of the earth taken out from the pit and then divide it by the area of the plot to find the height.
1. Calculate the volume of the pit:
The volume of a cuboid is given by the formula V = l × w × h, where l is the length, w is the width, and h is the height.
The length (l) of the pit is 10m, the width (w) is 8m, and the height (h) is 3m.
So, the volume (V) of the pit = 10m × 8m × 3m = 240 cubic meters.
2. Calculate the area of the plot:
The area of a rectangle is given by the formula A = l × w, where l is the length and w is the width.
The length (l) of the plot is 40m and the width (w) is 30m.
So, the area (A) of the plot = 40m × 30m = 1200 square meters.
3. Calculate the increase in level:
To find the increase in level, we divide the volume of the pit by the area of the plot.
Increase in level = Volume of pit / Area of plot
Increase in level = 240 cubic meters / 1200 square meters
Increase in level = 0.2 meters.
Therefore, the increase in the level of the plot is 0.2 meters.
To find the increase in the level of the plot, we need to calculate the volume of the earth that was taken out from the pit and spread on the rectangular plot.
The volume of the pit can be calculated by multiplying its length, width, and height:
Volume of the pit = length * width * height
= 10m * 8m * 3m
= 240 cubic meters
Now, let's calculate the area of the rectangular plot:
Area of the plot = length * width
= 40m * 30m
= 1200 square meters
Since the earth taken out from the pit is spread evenly on the plot, the increase in the level of the plot will be equal to the volume of the pit divided by the area of the plot:
Increase in level = Volume of the pit / Area of the plot
= 240 cubic meters / 1200 square meters
= 0.2 meters or 20 centimeters
Therefore, the increase in the level of the plot is 0.2 meters or 20 centimeters.
40(30)(height) = 10(8)(3)
height = 240/1200
= 1/5 m or .2 m or 20 cm