# Related time rates problem

#### wolfsprint

##### New member
The base of a rectangular box is square shaped. If the length of the base is increasing by 1cm/min and the height is decreasing by 2cm/min . Find this moment rate of change in the volume when the base length is 6cm and the height is is 24cm. Find how many minutes elapsed from this moment to vanish increase.

#### Ackbach

##### Indicium Physicus
Staff member
What ideas have you had so far? And could you please clarify your last sentence? I can't quite parse that.

#### wolfsprint

##### New member
I've thought of differentiate the volume of the rectangular square based, but I can't figure our what's its volume, and I think the last phrase means to find how many minutes elapsed from the moment that I calculate the rate of change in the volume till the increase stops or vanishes

#### wolfsprint

##### New member
Can you please solve it and show me the work?

#### Ackbach

##### Indicium Physicus
Staff member
I've thought of differentiate the volume of the rectangular square based, but I can't figure our what's its volume, and I think the last phrase means to find how many minutes elapsed from the moment that I calculate the rate of change in the volume till the increase stops or vanishes
How do you normally compute volume? What's the volume of a cube? What's the volume of a rectangular prism?

Can you please solve it and show me the work?
We don't operate that way here on MHB. Students do the heavy lifting, as they should. We help you get unstuck on a particular point or step.

#### wolfsprint

##### New member
Vol. Of the cube is L^3 and vol of regtangular prism is Lxwxh , but i still cant find this relevant

#### Ackbach

##### Indicium Physicus
Staff member
If the base is square-shaped, how does that change your volume formula?

#### wolfsprint

##### New member
i have no idea but ive read some where that a square based rectangular box is W^2h

#### Ackbach

##### Indicium Physicus
Staff member
i have no idea but ive read some where that a square based rectangular box is W^2h
That sounds like an idea to me! It is correct. So you have a formula for the volume:
$$V=w^{2}h.$$
What is the problem asking you to do?