Thread: Word problem involving differentiation..

A water tank has a rectangular base 1.5m by 1.2m. The sides are vertical and water is being added to the tank at a constant rate of 0.45m^3. At what rate is the depth of water in the tank increasing?

So far, I can say that dV/dt = 0.45, i.e. the rate of change in volume with respect to time is 0.45m^3 / minute.

I do know that the volume would be 1.5 x 1.2 x height.

But I cannot put things together..!

p.s. I have to use the chain rule.

Hello !

Originally Posted by struck

A water tank has a rectangular base 1.5m by 1.2m. The sides are vertical and water is being added to the tank at a constant rate of 0.45m^3. At what rate is the depth of water in the tank increasing?

So far, I can say that dV/dt = 0.45, i.e. the rate of change in volume with respect to time is 0.45m^3 / minute.

I do know that the volume would be 1.5 x 1.2 x height.

But I cannot put things together..!

p.s. I have to use the chain rule.

Let denote the depth of the water at time t.

Like you said, the volume would be :

Now if you differentiate both sides, not by using the chain rule but by using : , where a is a constant, it'll give :






and h'(t) is the rate of change of the depth !

Originally Posted by struck

A water tank has a rectangular base 1.5m by 1.2m. The sides are vertical and water is being added to the tank at a constant rate of 0.45m^3. At what rate is the depth of water in the tank increasing?

So far, I can say that dV/dt = 0.45, i.e. the rate of change in volume with respect to time is 0.45m^3 / minute.

I do know that the volume would be 1.5 x 1.2 x height.

But I cannot put things together..!

p.s. I have to use the chain rule.

What is /minute it is the volume that gets in one minute inside the tank, right? By how much would this volume increase the depth ? Volume/(Area of the base) or meters/minute