Question

Suppose we have a rectangular aquarium with dimensions of length 8 m, width 4 m and height
3 m. Suppose we are filling the tank with water at the rate of 0.4 mº/sec. How fast is the height
of water changing when the water level is 2.5m?​

Answer 1

The height of the aquarium is changing at the rate of 0.0125 m/sec.

Step-by-step explanation:

The volume of the rectangular aquarium with dimensions of length 8 m, width 4 m, and height 3 m is given by

V = LWH

Differentiating this equation with respect to time (t in seconds) we get,

⇒ $\frac{dV}{dt} = LW\times \frac{dH}{dt}$ ......... (1)

{Since L and W remains constant and only the height is changing}

Given that the tank is filling with water at the rate of 0.4 m³/sec.

Hence, from equation (1) we get,

$0.4 = 8 \times 4 \times \frac{dH}{dt}$

⇒ $\frac{dH}{dt} = 0.0125$ m/sec.

Therefore, the height of the aquarium is changing at the rate of 0.0125 m/sec. (Answer)