Question

A field is 40 m long and 30 m broad
In the centre of the field, a pit which
is 10 cm long and 2.5 m broad and 7m
deep has been dug out the earth taken
out of its is evenly spread over the
remaing part of the field. Find the
rise in the level of the field.​

Answer 1

Answer:

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] = 1175/175

⇒ [Rise in level of field] = 6.71 m

Thus, the field will rise up to a level of 6.71 m.