Chapter 1, Problem 42GP

To determine

The loss of depth of a lake per year.

Answer to Problem 42GP

8.76 cm per year

Explanation of Solution

Given:

Water consumption of family of four people per day is 1200 liter

Number of people in the town are 40,000

Area of lake, $A=50{\text{ km}}^2=50\times {10}^6{\text{ m}}^2$

Formula used:

Volume of the lake is given by,

  $V=A\times d$

Here, V is volume, A is area and d is depth.

So, depth is,

  $d=\frac{V}{A}$

Calculation:

Water consumption of one person per day $=\frac{1200}{4}=300\text{ liter}$

Thus, water consumption of one person per year,

  $=300\times 365=1.095\times {10}^5\text{ liter}$

Water consumption of 40,000 people $=1.095\times {10}^5\times \text{40,000 lites}=4.38\times {10}^9\text{ liter}$

Now, $1\text{ litre}={10}^{-3}{\text{ m}}^3$

Thus, volume of water used by 40,000 people is,

  $V=4.38\times {10}^6{\text{ m}}^3$

Substituting the values, we get

  $\begin{array}{l}d=\frac{4.38\times {10}^6{\text{ m}}^3}{50\times {10}^6{\text{ m}}^2}\\ \text{ = 0}\text{.0876 m}\\ \text{ = 8}\text{.76 cm}\end{array}$

Conclusion:

Thus, the depth of lake lose per year if its water is used by 40,000 people is $8.76\text{ cm}$