Answer:
[tex]9.2\ \text{m}[/tex]
Step-by-step explanation:
[tex]b[/tex] = Surface area of base = 5 square meters
Volume of water in tank = 70 cubic meters
The rate at which the volume is reducing is
[tex]\dfrac{dV}{dt}=2+4t\\\Rightarrow dV=2+4tdt[/tex]
Integrating from [tex]t=0[/tex] to [tex]t=3[/tex]
[tex]V=\int^3_0(2+4t)dt\\\Rightarrow V=2t+2t^2|_0^3\\\Rightarrow V=2\times 3+2\times 3^2-0\\\Rightarrow V=24[/tex]
Volume of water remaining in the tank is [tex]70-24=46\ \text{m}^3[/tex]
Suface area of base [tex]\times[/tex] depth = Volume
[tex]5\times d=46\\\Rightarrow d=\dfrac{46}{5}\\\Rightarrow d=9.2\ \text{m}[/tex]
The depth of the water remaining in the tank is [tex]9.2\ \text{m}[/tex].
