Calculating volumes of compound objects

This lesson develops the concept of calculating the volume of compound objects. In particular, students enhance their understanding of:

• Computing measurements using formulas.
• Decomposing compound shapes into simpler ones.
• Using right triangles and their properties to solve real-world problems.

The first activity looks at three glasses. The first has a bowl in the shape of a cylinder, the second has a bowl that starts as a cylinder and goes down into a hemisphere, the third has bowl in the shape of a cone. Students complete calculations on the volume of the bowls, and part filling them.

An extension activity looks at finding a formula for the volume of a bowl that is composed of a cylinder and cone. Hint sheets are provided, along with examples of student work to peer assess.

There are pre-lesson and post-lesson formative assessment tasks. Detailed teacher notes give suggestions on questioning and how to use the resources. Full solutions are given for each of the sections.

This is a concept development lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.