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

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Discussion Overview

The discussion centers around the problem of determining how the volume of a square-based box changes as its dimensions vary over time. Participants explore the implications of changing the base length and height on the volume, including the rates of change and the conditions under which the volume increase ceases.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant describes a scenario where the base length of a square box increases while the height decreases, prompting a need to find the moment rate of change in volume.
  • Another participant seeks clarification on the problem and expresses difficulty in understanding the phrasing of a specific sentence.
  • Several participants suggest differentiating the volume formula to find the rate of change, but there is uncertainty about the correct volume formula for a square-based box.
  • One participant proposes that the volume of a square-based rectangular box can be expressed as \( V = w^2 h \), indicating a potential formula for further calculations.
  • There is a request for a step-by-step solution to the problem, highlighting a desire for guidance in the problem-solving process.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the volume formula or the specific steps needed to solve the problem, indicating that multiple viewpoints and uncertainties remain in the discussion.

Contextual Notes

There are unresolved aspects regarding the application of the volume formula and the implications of the rates of change on the overall volume, as well as the specific conditions under which the volume increase stops.

Who May Find This Useful

This discussion may be useful for students studying calculus, particularly those interested in related rates and volume calculations for geometric shapes.

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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