Nothing in the real world is a plain cone or a plain cylinder — it's a toy, a tent, a rocket, a bird-bath. Snap two basic solids together and see which surfaces vanish, and why volume never lies the same way area does.
Every combination solid in this chapter is built from just five basic shapes. Move the shared dimensions below and watch every formula update at once — then scroll down to see what these blocks build in real life.
Tabs 02–04 explore these six real objects in detail.
A cone with its flat face joined to a hemisphere's flat face — round on top, pointed below.
A hemisphere sits on a cube's top face; the circle it covers disappears from the cube's area.
A cylinder capped at both ends by hemispheres of the same radius — no flat ends survive.
A hemisphere is scooped out of a cylinder's flat face, turning it into a depression instead of an addition.
A cone sits on top of a cylinder — sometimes with a narrower base, leaving a ring exposed.
A thinner cylinder is stacked on a wider one — same idea, just two of the same solid.
The golden rule: TSA of the combination = sum of only the surfaces you can actually touch from outside. Any flat face buried where two solids join drops out of the count.
Volume is more forgiving than area: volume of the combination = sum (or difference) of the volumes of its parts. Nothing "disappears" the way flat faces do for surface area.
Three build sheets from the chapter — a two-tone rocket, a canvas tent, and an iron pole priced by weight.