Square based prism general rule

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For a square-based prism, the surface area and volume formulas are simplified to Surface Area = 2(s^2 + 2sh) and Volume = s^2h, where s is the side length of the square base and h is the height. The discussion emphasizes that one cannot apply rectangular prism formulas directly to square-based prisms due to their specific characteristics. Participants express uncertainty about how to approach the problem, indicating a need for clarification on the formulas and their application. The conversation also hints at a transition to calculus-related topics, suggesting a broader mathematical context. Understanding the unique properties of square-based prisms is crucial for solving related problems effectively.
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Homework Statement


See attached picture

Homework Equations



For any rectangular prism, the formulas are the following:

Surface Area = 2(lw + wh + hl); l is length, w is width, and h is height.

Volume = lwh; l is length, w is width, and h is height.

For a square-based prism, the formulas are simplified into the following:

Surface Area = 2(s^2 + 2sh); s is side of square face and h is height.

Volume = s^2h; s is side of square face and h is height.

The Attempt at a Solution


I'm not sure how to start the question at all[/B]
 

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You can't use a formula for a specific subgroup (rectangular prisms) for your square-based prisms ! The latter are more general than just rectangular.

Is there anything you did or found in question 2 that is relevant for the current exercise ?
 
I don't have the question and answe on me but I will post it tomorrow
Thanks for replying, I've no idea how to do this and it's bugging me
 
Well, some good spirit warned you (for obvious reasons), but also moved to the calculus part of PF. Why would that be ?
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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