How Does the Volume Change as Dimensions of a Square-Based Box Alter?

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SUMMARY

The discussion focuses on calculating the rate of change of the volume of a square-based box as its dimensions change. The volume formula for a square-based box is established as V = w²h, where w is the width of the base and h is the height. Given that the base length increases at 1 cm/min and the height decreases at 2 cm/min, the moment rate of change in volume is to be calculated when the base length is 6 cm and the height is 24 cm. The discussion also addresses the time until the volume increase ceases.

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wolfsprint
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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.
 
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What ideas have you had so far? And could you please clarify your last sentence? I can't quite parse that.
 
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
 
Can you please solve it and show me the work?
 
wolfsprint said:
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?

wolfsprint said:
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.
 
Vol. Of the cube is L^3 and vol of regtangular prism is Lxwxh , but i still can't find this relevant:(
 
If the base is square-shaped, how does that change your volume formula?
 
i have no idea but I've read some where that a square based rectangular box is W^2h
 
wolfsprint said:
i have no idea but I've 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?
 

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