Related Rates problem?

[bobotheclown]

Water is being poured into a fish tank at the rate of 3 ft^3 / min. How fast is the water level rising if the base of the tank is a rectangle which is 2 ft x 3 ft?

No idea where to begin.

 

[bobotheclown]

You are changing the volume of water added to the thank and what you want to measure is the height of the water above the bottom.

you have dV/dt = 3 cu ft/min

the volume of the water in a rectangular tank is given by A h, where A is the area of the base of the tank and h is the height of the water in it.

A is given to be 2x3 = 6 sq ft.

so V is 6 h cu ft

and h = V/6

now differentiate with respect to t on both sides.

See if you can figure it out from here.

I got 1/2 ft per min = dh/dt

Hopefully that's correct.