Thank you for using the site. I'll be happy to help you with this. I have a couple of brief questions to ask first though.
1. When you say that this piece of metal is "semi-circular", can you be more specific? It this a flat piece of metal that is a half-circle, like a pizza that has been cut in half? Or is it a curved plate that is the shape of half of a cylinder, like a pipe that has been sliced in half length-wise?
2. How are the prices for the three metals quoted? Are they given in units of money per square centimeter, or in units of money per cubic centimeter?
Yes, I see what you mean about having limited information.
I would assume that the prices for the metals are quoted as a price per mass (kilograms), or a price per volume (cubic meters or cubic centimeters).
How about if I write up procedures for calculating surface area and volume for both proposed shapes, and then methods for calculating price based on mass and volume. That way you should have all of the bases covered and you can pick and choose which parts to use?
What age group will you be presenting this to (so I can tailor the writing style)?
Ok, so around late high school / early college age here in the US. I'll get working on this and will have a Word document posted for you as quickly as I can. You should receive an email notification when the file is posted. Should you have any follow-up questions to ask once you've reviewed the document, please don't hesitate to ask. I'll be happy to explain anything that is not clear.
Once I got started on this and drew some diagrams, I realized that the "half-cylinder" scenario was unlikely to be needed since no mention was made of any length (or height) of the object. Given the thickness of the semi-circular piece, the only remaining unknown would be the actual diameter, which seems like the simplest interpretation. Should it turn out that you actually need the calculations for a semi-cylindrical object, please let me know and I'll be happy to add that in (no additional charge). I just didn't want to throw too much unnecessary information in here and have it lead to confusion.
Please take a look at the document at the link below and let me know if there is anything that requires clarification: