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

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In summary, the problem is asking for the rate of change in volume of a rectangular box with a square-shaped base, with the base length increasing by 1cm/min and the height decreasing by 2cm/min when the base length is 6cm and the height is 24cm. It also asks to find the number of minutes elapsed from the moment the rate of change is calculated until the increase in volume stops. The idea the student has had so far is to use the formula for volume of a square-based rectangular box, which is w^2h, but they are unsure of how to proceed.
  • #1
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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  • #2
What ideas have you had so far? And could you please clarify your last sentence? I can't quite parse that.
 
  • #3
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
 
  • #4
Can you please solve it and show me the work?
 
  • #5
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.
 
  • #6
Vol. Of the cube is L^3 and vol of regtangular prism is Lxwxh , but i still can't find this relevant:(
 
  • #7
If the base is square-shaped, how does that change your volume formula?
 
  • #8
i have no idea but I've read some where that a square based rectangular box is W^2h
 
  • #9
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?
 

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

1. What is a related time rates problem?

A related time rates problem is a type of mathematical problem that involves finding the rate of change of one quantity with respect to another quantity over a specific period of time. It is often used to solve real-world problems involving speed, distance, and time.

2. How do you approach a related time rates problem?

The first step in approaching a related time rates problem is to identify the quantities involved and their respective units of measurement. Then, set up a proportion or equation that relates the quantities and use the given information to solve for the unknown rate.

3. What are some examples of related time rates problems?

Examples of related time rates problems include calculating the average speed of a car on a road trip, determining the rate at which water is filling up a swimming pool, and finding the time it takes for a train to travel a certain distance.

4. What are some common mistakes to avoid when solving related time rates problems?

One common mistake is to mix up the units of measurement, which can lead to incorrect solutions. It is also important to pay attention to the direction of the rates, as they can be either increasing or decreasing. Another mistake is to use the wrong formula or equation for the given problem.

5. How can understanding related time rates problems be useful in real life?

Understanding related time rates problems can be useful in many real-life situations, such as planning travel routes and schedules, managing production or work rates, and budgeting time and resources. It can also help in analyzing trends and changes over time, such as in economics or scientific research.

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