Question

why should I divide the volume of Earth dug out by area on which the earth is spread to find out the rise in level of the field? shouldn't it be the other way round?

Answer 1

it is because area left over*height=volume of pit(as it is uniformally spread)
i.e (LB)*H=lbh
     H=volume of earth dug out /area left over
           https://hi-static.z-dn.net/files/da3/5c4a344bf6d5136b20860c6c8034ed01.jpeg
           ;hope this helps

Answer 2

Hey frnd ,
Good question . Let me help you to clear this out . Don't cram the formula , always understand how it comes. Here I go,

First of all you have to find the height of the field which is increased due to the spreading process of earth which is dug out.

Now , volume of the earth ( mud or sand) taken out from the ground should be equal to volume of the field on which it is spread .

Actually mud or sand in the pit takes the shape of cuboid
So volume of the earth dug out = volume of the cuboid formed by sand in pit , i.e 400 m^3 .

Now the sand taken out of the pit is spread out on the field.
Here , I will explain you the shape of field with a illustration.
Consider a cuboidal cake which is cut out from the side . The cut out piece is cuboidal . Now the shape of the the field is the cuboidal cake with a small piece of cuboidal shape cutted out , say with a knife .

So, base area of this field ( which is area of rectangle - area of side rectangle formed by pit) × height of the field = volume of the field
As u know volume of field = volume of the cuboid formed by mud in the pit .

Now , base area of field (area on which earth is spread) × height of the field ( rise in the level of field) = volume of earth dug out

So , height of field = volume of earth dug out / base area of the field
.

Always remember volume of any figure is base area stacked to the height h . Eg , volume of cuboid is base area i.e area of rectangle stacked to the height h . So volume becomes ( base area i.e lb)×height(h)




I hope it helps . Pls mark me brainliest .