500 persons take a dip in a cuboidal pond \(80\,\text{m}\times50\,\text{m}\). If the average water displacement per person is \(0.04\,\text{m}^3\), find the rise in water level.
0.5 cm
Step 1: Find the total volume of water displaced.
Each person displaces \(0.04\,\text{m}^3\) of water.
For 500 persons, total displaced volume:
\(500 \times 0.04 = 20\,\text{m}^3\).
Step 2: Relating displaced volume to rise in water level.
The pond has a rectangular (cuboidal) shape with length = \(80\,\text{m}\) and breadth = \(50\,\text{m}\).
Base area of the pond = length × breadth:
\(80 \times 50 = 4000\,\text{m}^2\).
If water rises by \(h\,\text{m}\), the extra volume added = base area × height rise = \(4000 \times h\).
Step 3: Equating volumes.
Total displaced volume = Extra volume of pond water.
So, \(4000h = 20\).
\(h = \dfrac{20}{4000} = 0.005\,\text{m}\).
Step 4: Convert to cm.
\(0.005\,\text{m} = 0.005 \times 100 = 0.5\,\text{cm}\).
Final Answer: The water level rises by 0.5 cm.