How much would the water level decline if a cuboidal reservoir, measuring 7 metres in length, 6 metres in width, and 15 metres in height, is connected to pumps that are used to remove 8400 litres of water from the reservoir?

Given dimensions of the cuboidal reservoir:

Length (l) = 7 meters
Width (w) = 6 meters
Height (h) = 15 meters

The initial volume of the reservoir (before pumping out 8400 litres = l × w × h

= 7 × 6 × 15 = 630 m³

We know the volume of water to be removed = 8400 litres

= 8.4 m³     [1 m³ = 1000 liters]

Final Volume = Initial Volume - Volume to be removed

Final Volume = 630 - 8.4 = 621.6 m³

Let the height of the reservoir after pumping be 'h'.

So, 7 × 6 × h = 621.6

⇒ h = 621.6/42 = 14.8 m

So, the water level declined = Initial height - Final height = 15 - 14.8 = 0.2 m

Therefore, the water level would decline by approximately 0.2 metres in the cuboidal reservoir after removing 8400 litres of water.