Question

Explain how a coke bottle is similar and or different than calculating the volume of a rectangular prism?

Answer 1

Rectangular prism has a uniformity missing in a Coke bottle. In the prism, the area is the same throughout. This means we just measure the base area, multiply by the height, and are done.

In the Coke bottle, the area is a function of z, the height above the base. This means we have to use a more sophisticated method (usually integral calculus) to get the exact answer.

We might be able to estimate the volume by partitioning the Coke bottle cleverly, say at the local maximum and minimum diameters, estimate the average size and distance in z between those points, and add the volumes together. We could probably come close enough for many applications, but wouldn't have an exact answer.

Answer 2

How did I do?

Answer 3

you did great. thank you