1.) What is the formula for the surface area of a rectangular prism?
2.) What would it's derivative be?
3.) What would the critical numbers be?
I know it seems like a lot for one question but it's a part of a much bigger problem and need this part but I keep getting a wack answer. Thanks to any anyone who responses. I appreciate any answers.
Update:The original problem compares the surface area of a cylindrical container to that of a rectangular prism. I'm trying to find out which one has the lowest surface area. For the rectangular prism I'm using 2 equations:
1.) Volume = LWH
2.) Surface area = ?
So it's basically an optimization problem. Imma plug in the Volume in the Surface Area equation and hopefully get the right answer. But right now Im having trouble with the Surface Area equation. The given information I have is V=946 ml, and W = 5cm. I don't know if Im doing the problem right or not so and help would be much appreciated. Thank You
Answers & Comments
Verified answer
You have a formula for S in terms of L,W, and H.
when you ask for the derivative of S, do you mean dS/dL,
dS/dW, or dS/dH ?
And whichever you mean, are the other two dimensions constant? Or are they also functions of the variable with respect to which you are differentiating? If the latter is the case, then you have to worry about the chain rule. For example, dS/dL would involve dW/dL and dH/dL.
You need to give us more info about the problem. What are the variables, what are the constants, what variables are functions of what other variables, and what is the independent variable for purposes of differentiation?
(If the bigger problem has this prism incscribed in, say, a sphere, or the problem otherwise puts some conditions on the dimensions, then you have extra information relating the dimensions to each other.)
Base shape: Rectangle, length 'L' and width 'W'
Area of base: L Ã W
Perimeter of base: 2(L+W)
Surface area = 2LW + 2(L+W)H