A field is 40m long and 30m broad. in the centre of the field, a pit which is 10m long & 2.5m broad & 7m deep has been dug out. the earth dug out is spread over the remaining part of the field. find the rise in the level of the field.
Answers
If a 10 m x 2.5 m x 7 m pit is dug out of 40 m * 30 m rectangular field, then the level of the field will rise up to 6.71 m.
Step-by-step explanation:
Step 1:
Length of the field = 40 m
Breadth of the field = 30 m
∴ The area of the field = Length x Breadth = 40 * 30 = 1200 m²
Step 2:
Dimensions of the rectangular pit:
length = 10 m
breadth = 2.5 m
height = 7 m
∴ The area of the base of the pit = l * b = 10 * 2.5 = 25 m²
∴ The area of the remaining part of the field (i.e., excluding the pit) is given by,
= [The area of the field] – [The area of the base of the pit]
= 1200 – 25
= 1175 m²
Step 3:
Now, it is given that the amount of earth dug out of the pit was spread over the remaining part of the field, so
[Volume of the rectangular pit] = [Area of the remaining part of the field] * [Rise in the level of the field]
Therefore, we can write
10 * 2.5 * 7 = 1175 * [Rise in level of field]
⇒ 175 = 1175 * [Rise in level of field]
⇒ [Rise in level of field] =
⇒ [Rise in level of field] = 6.71 m
Thus, the field will rise up to a level of 6.71 m.
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