Question

In the middle of a rectangular field measuring 30m × 20m, a well of 7 m diameter and 10 m 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.

Answer 1

Are you sure the question has only these many values

Answer 2

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$<i>$The rise in the level of the field is 68.6 m .

Step-by-step explanation:

SOLUTION :  

Given :  

Length of a rectangular field , l= 30 m

Breadth of a rectangular field , b = 20 m

Height of a well , H = 10 m

Diameter of a well = 7m

Radius of a well, r = 7/2 = 3.5 m

Let the rise in the level of the field be h meters.

Volume of the earth dug out (well) = πr²h

= 22/7 × 3.5 × 3.5 × 10

= 22 × 0.5 × 3.5 × 10

= 22 × 5 × 3.5

Volume of the earth dug out = 385 m³

Area of the field = l × b = 30 × 20

Area of the field = 600 m²

Area of the base of the well = πr²  

= 22/7 × 3.5²

Area of the base of the well= 38.5 m²

Area of the remaining part of the field = Area of the field - Area of the base of the field

= 600 - 38.5  

Area of the remaining part of the field = 561.5 m²

Volume of the raised field = Area of the base × Height

= 561.5 × h  

Volume of the raised field = Volume of the earth dug out  

561.5 × h = 385

h = 385/561.5 = 0.686 m

h =  0.686 m × 100 = 68.6 m

h = 68.6 m  

Hence, the rise in the level of the field is 68.6 m .

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