Question

The length and breadth of a rectangular field are }54 m and 121 m respectively. If by digging a hole of length 14 m and breadth 11 m in the middle of the field, the soil thus obtained is dispersed in the remaining land, then the height of the field is increased by 25 cm. Determine the depth of the hole.

Answer 1

The total suface area of the field `=154 xx 121` sq-metres = 18634 sq-metres.
-Again, the surface area of the hole `=(14 xx 11)` sq-cm = 154 sq-cm
So, the suface ar of the ramianing field =(18634-154) sq-cm=18480 sq-cm .
The height of the fiedl is raised by 25 cm. `=25/100 ` m `= 1/4` m
So, the volume of the disperse soil `=(18480 xx 1/4) `cu -m =4620 cu-m
Let the depht of the hole of x m.
`therefore 14 xx 11 xx x =4620 ` or, `x=(4620)/(14 xx 11)=30`
Hence the depht of the hole was 30 m