Question

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?

Answer 1

\[\text{ The dimensions of the plot dug outside the field are 50 m } \times 30 m \times 8 m . \]

\[\text { Hence, volume of the earth dug - out from the plot = 50 } \times 30 \times 8 = 12000 m^3 \]

\[\text { Suppose that the level of the earth rises by h m } . \]

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

\[\text { Volume of earth dug - out = 150 } \times 100 \times h\]

\[ \Rightarrow 12000 = 15000 \times h\]

\[ \Rightarrow h=\frac{12000}{15000}=0.8 m\]

\[ \Rightarrow h = 80 cm ( \because 1 m = 100 cm)\]

\[\therefore \text { The level of the field will rise by 80 cm }.\]