As they did with cylinders in a previous lesson, students in this lesson use the formula \(V=\frac13 \pi r^2 h\) to find the radius or height of a cone given its volume and the other dimension. Then they apply their understanding about the volumes of cylinders and cones to decide which popcorn container and price offers the best deal. Depending on the amount of guidance students are given, this last activity can be an opportunity to explain their reasoning and critique the reasoning of others (MP3).
- Calculate the value of one dimension of a cylinder, and explain (orally and in writing) the reasoning.
- Compare volumes of a cone and cylinder in context, and justify (orally) which volume is a better value for a given price.
- Create a table of dimensions of cylinders, and describe (orally) patterns that arise.
Let’s figure out the dimensions of cones.
- I can find missing information of about a cone if I know its volume and some other information.
A cone is a three-dimensional figure like a pyramid, but the base is a circle.
A cylinder is a three-dimensional figure like a prism, but with bases that are circles.
A sphere is a three-dimensional figure in which all cross-sections in every direction are circles.