Need Help! "Your task is to determine which shape maximises the volume of water that can be held by a gutter of a fixed length of material."

[Math student1324]

I have been assigned a task where I do not know where to start the task is as follows

Your task is to determine which shape maximises the volume of water that can be held by a gutter of a fixed length of material.
choose a suitable fixed length for the cross section and explore different shapes.
You should consider a rectangular, triangular and round gutter as well as at least 2 other shapes.
Determine the dimensions and cross-sectional area that maximises the water held by the gutter for each shape.
Generalise each shape for a length L and make use of calculus to determine the dimensions of the shape and associated cross-sectional area that optimises the water held by the gutter.

what mathematical method do I approach this question with what constraints do I use? My peers all are using different methods and I don't which one to use some are using a perimeter and some are using a surface area which one is easier I have been able to do some sort of working out for the rectangular gutter and triangle however they are not coherent enough to hand in to the teacher. Furthermore, I cant get started with the semicircle gutter. Does anyone know how to go about this investigation?

 

[khansaheb]

I have been assigned a task where I do not know where to start the task is as follows

Your task is to determine which shape maximises the volume of water that can be held by a gutter of a fixed length of material.
choose a suitable fixed length for the cross section and explore different shapes.
You should consider a rectangular, triangular and round gutter as well as at least 2 other shapes.
Determine the dimensions and cross-sectional area that maximises the water held by the gutter for each shape.
Generalise each shape for a length L and make use of calculus to determine the dimensions of the shape and associated cross-sectional area that optimises the water held by the gutter.

what mathematical method do I approach this question with what constraints do I use? My peers all are using different methods and I don't which one to use some are using a perimeter and some are using a surface area which one is easier I have been able to do some sort of working out for the rectangular gutter and triangle however they are not coherent enough to hand in to the teacher. Furthermore, I cant get started with the semicircle gutter. Does anyone know how to go about this investigation?

What property needs to be maximized given a fixed length (constraint)?

What are the unknowns (variables) of this problem?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

 

[Dr.Peterson]

My peers all are using different methods and I don't which one to use some are using a perimeter and some are using a surface area which one is easier

Don't worry about what others are doing. What is it that the problem asks you to maximize? Tell us your ideas about it.

It's not an issue of what's easier, but of what's correct (mostly).

I have been able to do some sort of working out for the rectangular gutter and triangle however they are not coherent enough to hand in to the teacher.

That's fine; your first attempt won't be the final draft. Just show us whatever you did, and tell us what you think is missing.

Furthermore, I cant get started with the semicircle gutter. Does anyone know how to go about this investigation?

There's probably a good reason for this being different from the others; there are fewer parameters to vary. Just show us whatever you can, even if you find that there is nothing to maximize.