Question

a rectangular tank of dimensions 24m by 12m by 8m is dug inside a rectangular field 600m long and 200m broad. the earth taken out is evenly spread over the field. by how much will the level of the field rise​

Answer 1

If a 24m x 12m x 8m tank is dug out of 600m * 200m rectangular field, then the level of the field will rise up to 1.92 cm.

Step-by-step explanation:

Step 1:

Length of the rectangular field = 600 m

Breadth of the rectangular filed = 200 m

∴ The area of the rectangular field = Length x Breadth = 600 * 200 = 120000 m²

Step 2:

For the rectangular tank:

Length = 24 m

Breadth = 12 m

Height = 8 m

∴ The area of the base of the tank = l * b = 24 * 12 = 288 m²

∴ The area of the rectangular field excluding the tank is given by,

= [The area of the rectangular field] – [The area of the base of the tank]

= 120000 – 288

= 119712 m²

Step 3:

Now, it is given that the amount of earth taken was used to level the rectangular field, so

[Volume of the rectangular tank] = [Area of the rectangular field excluding the tank] * [Rise in level of field]

Therefore, we can write  

24*12*8 = 119712 * [Rise in level of field]

⇒ 2304 = 119712 * [Rise in level of field]

⇒ [Rise in level of field] = 0.0192 m = 1.92 cm

Thus, the filed will rise up to a level of 1.92 cm.

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Also View:

In the middle of a rectangular field measuring 30m x 20m, a well of 7m diameter and 10m depth is dug. The earth so removed is evenly spread over the remaining part of the field. Find the height through which the level of the field is raised.

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