Question

how fast is the water level rising in a rectangular fish tank whose base is 20 ft^2 if the tank is being filled at a rate of 0.5ft^3/min

Answer 1

Answer: the water level rises by 0.025ft each min

Step-by-step explanation:

The volume of a rectangular fish tank is:

V = height*base

then if the hwight is 1 ft, we have that the volume is:

V = 1ft*20ft^2 = 20ft^3

Now, the amount of water that enters in the tank is r = 0.5ft^3/min

now, the change in the heigth will be

change in volume = r =change in height*base

r/base = height.

(0.5ft^3/min)/20ft^2 = change in height = 0.025ft/min

This means that the water level rises by 0.025ft each min

Answer 2

V = Bh
0.5 ft^3 = (20 ft^2)h
h = (0.5 ft^3)/(20 ft^2) = 0.025 ft

The rate of change of water depth is 0.025 ft/min.