A TRENCH OF 2.5 MTS AND DEPTH OF 2 MTS IS DUG OUTSIDE AN RECTANGLE FEILD OF LENGTH OF 250 MTS AND BREADTH OF 200 MTS. THE MUD FROM THE TRENCH WAS EVENLY DISTRIBUTED IN THE RECTANGULAR FIELD. FIND THE INCREASE IN THE HEIGHT OF THE FIELD.
To find the increase in the height of the field, we first need to calculate the volume of the mud that was evenly distributed in the rectangular field.
1. Start by finding the volume of the trench:
Volume of the trench = length × width × depth
Volume of the trench = 250 m × 200 m × 2.5 m
Volume of the trench = 125,000 m³
2. Next, find the volume of the rectangular field:
Volume of the rectangular field = length × width × height
We want to find the increase in height, so initially, the height is 0 m.
Volume of the rectangular field = 250 m × 200 m × 0 m
Volume of the rectangular field = 0 m³
3. Add the volume of the trench to the initial volume of the field to get the final volume:
Final volume = Volume of the rectangular field + Volume of the trench
Final volume = 0 m³ + 125,000 m³
Final volume = 125,000 m³
4. Now, we can find the new height of the field by rearranging the volume formula:
Volume = length × width × height
height = Volume / (length × width)
height = 125,000 m³ / (250 m × 200 m)
height = 125,000 m³ / 50,000 m²
height = 2.5 m
Therefore, the increase in the height of the field is 2.5 meters.