Question

if you were to extract 15000 mcubic from a lake each year for 15 years, how far would the lake level fall? total volume of water given as 5400000 m cubic and water depth of the lake is 4 m

Answer 1

`d=0.17m`

Step-by-step explanation: Each year a volume of 15,000 cubic meters is taken from the lake for 15 years, the lake has a surface area of 1.35 square kilometers and a depth of 4m. We have to find the fall in the depth of the river after 15 years:

The total water taken out of the lake in 15 years is:

`\begin{gathered} T=(15,000m^3)*15=225,000m^3 \\ \\ T_w=225,000m^3 \end{gathered}`

Therefore the fall in height is:

`\begin{gathered} A* d=(225,000m^3) \\ \\ \\ A=1.35km^2=1,350,000m^2 \\ \\ \\ A=1,350,000m^2 \\ \\ \\ \therefore\Rightarrow \\ \\ \\ (1,350,000m^2)d=(225,000m^3) \\ \\ \\ \\ d=((225,000m3))/((1,350,000m^2))=0.1666666666 \\ \\ \\ \\ d\approx0.17m \\ \end{gathered}`

Therefore the height of the lake will reduce by 0.17me.