Hello, I am a student in BC Calculus, and for a project we were asked to bring in a can of our choice and take measurements. Following the measurements, we calculated the minimum amount of surface area the tin can could have, while still having the same volume.
The can I brought in was bought at Stop and Shop, and it was the Black Pitted Ripe Olives small. Upon my calculations, I concluded that you are able to decrease the surface area while keeping the same volume, saving 5.7829695607438 cm^2. You can reduce the surface area by that much if you reduce the height of the can by 2.582719345371278 cm and increase the radius by .529837187418061 cm, then you can do so.The final height would be 8.6672806546287722 cm and the final radius would be 4.333640327314. This difference means that for about every 71 cans you could have made one more can, so if you are producing thousands, say 71,000, you could actually have made an extra 1,000 cans with the same amount of resources, increasing revenue on that product.
I appreciate you taking the time to read this, I hope that my calculations helped in someway.
I am very eager to recieve a response, and learn more about the process. Thank you.