M4.5.1 For the adult
Prisms and cylinders
How much does a tin hold, and how much metal is in it?
What this chapter teaches
A prism keeps the same cross section all the way along, so its volume is the area of that cross section times its length. A cylinder is a circle stretched along its height, so V = πr²h. Its total surface is the curved rectangle, 2πrh, plus two circles, 2πr².
Three questions to ask
There is no one right wording. Listen for the idea.
- Why do we find the area of the end face before we multiply by the length?
- Where does the 2πr in the curved surface of a cylinder come from?
- If the radius of a cylinder doubles and the height stays the same, what happens to its volume, and why?
After the chapter, the learner can
- Find the volume of a prism as end area × length
- Find the volume and surface area of a cylinder
What they copy into their notebook
Prism: volume = end area × length. Cylinder: V = πr²h. Curved surface 2πrh. Two ends 2πr². Use the radius, not the diameter.