Surface Area of Solids

Picturing the net, children add the two bases and all the side faces to get the outside area of a solid. The sequence runs through rectangular prisms and cubes, triangular prisms, trapezoidal prisms, pentagonal prisms, cylinders and half cylinders, and reaches composite solids such as a rectangular prism minus a cylinder, a concentric pipe, and a cylinder with a C-shaped slit.

Finding the side face of a cylinder by multiplying the diameter, rather than the circumference, by the height stands out. Many answers add only one base and fall short by exactly one base area. With a solid that has a hole through it, children subtract the faces that disappeared but forget to add the inner tube surface the hole creates.

The focus switches from how much fills a solid to how much surface wraps around it. The same solid shapes handled in Volume of Prisms and Cylinders are looked at again here with a different formula. Proportion and Inverse Proportion, which follows, moves to an entirely different question: how two quantities change together.