M4.5.4 For the adult
Joined and cut solids
How much does a flower pot hold, when it is a cone with its tip cut off?
What this chapter teaches
A joined solid is split into parts whose volumes are added. A cone with its tip cut off is the whole cone minus the small cone that was cut away. The small cone is similar to the whole cone, so similar triangles give its height.
Three questions to ask
There is no one right wording. Listen for the idea.
- How would you find the volume of a pencil that is a cylinder with a cone at one end?
- Why is the cut-off tip of a cone similar to the whole cone?
- If a cone is cut halfway up, what fraction of its volume is the tip, and why?
After the chapter, the learner can
- Find the volume of a cone with its tip cut off
- Find the volume of a solid made of a cylinder and a cone
What they copy into their notebook
Joined solid: add the parts. Cut solid: subtract the part that is gone. Frustum = big cone − small cone. Similar triangles give the missing height.