Modeling with Functions

Each of the problems below is a link. If you click on the problem, it will take you to a YouTube video of a full, step-by-step solution for the problem. You may try these problems as practice and use the videos to check your answer, or you can just watch the videos to see more worked-out example problems.

1. The height of a circular cylinder is four times its radius. Find a function that models its volume V in terms of its radius r. Find its volume if its radius is 2 in (round to the nearest tenth of a cubic inch). Find its radius if its volume is 200 cubic inches (round to the nearest tenth of an inch).
2. A rectangle has a perimeter of 36 meters. Find a function that models its area A in terms of the length x of one of its sides. Is it possible for the rectangle to have an area of 72 square meters? If so, find its dimensions. Is there a maximum area that the rectangle can have? If so, find it.