Question

A well is dug 10m deep and 7m diameter in the corner of a field 20m long and 15m wide. The earth dug out is spread over the remaining field. Find the rise of the field.

Answer 1

If the earth from the well is dug out is spread over the remaining field then the rise of the field is 1.47 m.

Step-by-step explanation:

Step 1:  

The length of the rectangular field = 20 m

The breadth of the rectangular field = 15 m

∴ Area of the rectangular field = 20 * 15 = 300 m²  

Step 2:

The diameter of the well = 7 m

∴ Radius = $\frac{7}{2}$ m

The height of the well = 10 m

Therefore,  

Area of base of the well = πr² = (22/7)*(7/2)² = 11/2 = 38.5 m²

And,

Volume of the well = [Area of base of the well] * [height of the well] = 38.5 * 10 = 385 m³

Step 3:

Now,

The area of the remaining field is given by,

= [Area of the rectangular field] – [Area of the well]  

= 300 – 38.5

= 261.5 m²

It is given that the volume of earth dug out from the well is spread on the remaining portion of the field, therefore, we can write  

The volume of the well = [Area of the remaining portion of the field] * [Rise in height of the field]

⇒ 385 = 261.5 * [Rise in height of the field]

⇒ Rise in the height of the field = $\frac{385}{261.5}$ = 1.47 m

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Also View:

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