A field is 150 m long and 100 m wide.


A field is 150 m long and 100 m wide. A plot (outside the field) 50 m long and 30 m wide is dug to a depth of 8 m and the earth taken out from the plot is spread evenly in the field. By how much is the level of field raised?


The dimensions of the plot dug outside the field are $50 \mathrm{~m} \times 30 \mathrm{~m} \times 8 \mathrm{~m}$.

Hence, volume of the earth dug - out from the plot $=50 \times 30 \times 8=12000 \mathrm{~m}^{3}$

Suppose that the level of the earth rises by $\mathrm{hm}$.

When we spread this dug - out earth on the field of length $150 \mathrm{~m}$, breadth $100 \mathrm{~m}$ and height $\mathrm{h} \mathrm{m}$, we have:

Volume of earth dug $-$ out $=150 \times 100 \times \mathrm{h}$

$\Rightarrow 12000=15000 \times \mathrm{h}$

$\Rightarrow \mathrm{h}=\frac{12000}{15000}=0.8 \mathrm{~m}$

$\Rightarrow \mathrm{h}=80 \mathrm{~cm} \quad(\because 1 \mathrm{~m}=100 \mathrm{~cm})$

$\therefore$ The level of the field will rise by $80 \mathrm{~cm}$.

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