a rectangular plot is 24 m long and 20m wide. A cubical pit of edge 4m is dug at each of the four corners of the field and the soil removed is evenly spread over the remaining part is of the plot. By what height does the remaining plot get raised??
Answers
If a cubical pit is dug out from four corners of the 24 m * 20 m rectangular plot, then the height by which the remaining plot get raised is 0.615 m or 6.15 dm.
Step-by-step explanation:
Step 1:
Length of the rectangular plot = 24 m
Breadth of the rectangular plot = 20 m
∴ The area of the rectangular plot = Length x Breadth = 24 * 20 = 480 m²
Step 2:
The edge of the cubical pit, a = 4 m
∴ The area of the base of four such cubical pits = 4 * a² = 4 * 4² = 64 m²
∴ The area of the remaining part of the rectangular plot (i.e., excluding the 4 pits) is given by,
= [The area of the rectangular plot] – [The area of the base of the 4 cubical pits]
= 480 – 64
= 416 m²
Step 3:
Now, it is given that the amount of earth taken out from each of the pit was used to level the remaining part of the rectangular plot, so
[Volume of 4 cubical pits] = [Area of the remaining part of the rectangular plot] * [Rise in the level of the remaining part of the plot]
Therefore, we can write
4 * a³ = 416 * [Rise in the level of the remaining part of the plot]
⇒ 4 * 4³ = 416 * [Rise in the level of the remaining part of the plot]
⇒ 256 = 416 * [Rise in the level of the remaining part of the plot]
⇒ [Rise in the level of the remaining part of the plot] = 256/416
⇒ [Rise in the level of the remaining part of the plot] = 0.615 m or 6.15 dm.
Thus, the filed will rise up to a level of 0.615 m or 6.15 dm.
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