Question

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.

Answer 1

$\text{Length of a field (l)}=200m$

$\text{Breadth (b)}=150m$

$\text{Length of plot}=50m$

$\text{and breadth}=40m$

$\text{Depth of plot}=7m$

$\therefore \text{Volume of earth dug out of the plot}$$=50\times 40\times 7m^3$

$=14000m^3$

$\text{Area of field}=200\times 150m^2$

$=30000m^2$

$\text{Let the height of earth spread on the field}=h$

$\therefore Volume=Area\times Height$

$\therefore 30000\times h=14000$

$h=\frac{14000}{30000}=\frac{7}{15}m$

$=0.47mor47cmapprox$