A field is $200\ m$ long and $150\ m$ broad. There is a plot, $50\ m$ long and $40\ m$ broad, near the field. The plot is dug $7\ m$ deep and the earth taken out is spread evenly on the field. By how many metres is the level of the field raised? Give the answer to the second place of decimal.

Given:

A field is $200\ m$ long and $150\ m$ broad. There is a plot, $50\ m$ long and $40\ m$ broad, near the field. The plot is dug $7\ m$ deep and the earth taken out is spread evenly on the field. 

To do:

We have to find the height of the field raised.

Solution:

Length of the field $(l) = 200\ m$

Breadth of the field $(b) = 150\ m$

Length of the plot $= 50\ m$

Breadth of the plot $= 40\ m$

Depth of the plot $= 7\ m$

Therefore,

Volume of the earth dug out of the plot $=l b h$

$=50 \times 40 \times 7$

$=14000 \mathrm{~m}^{3}$

Area of the field $=200 \times 150$

$=30000 \mathrm{~m}^{2}$

Let the height of the earth spread on the field be $h$.

This implies,

Volume of the earth dug out $=$ Area of the field $\times$ Height

$30000 \times h=14000$

$h=\frac{14000}{30000}$

$h=\frac{7}{15} \mathrm{~m}$

$=0.47 \mathrm{~m}$

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Updated on: 10-Oct-2022

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