SM3.2 Surface areas and volumes
You can find surface areas and volumes of solids built by joining or carving cones, cylinders, spheres and cuboids, and handle conversions where a solid is melted and recast.
Topics shown in module order.
The solids of earlier classes come back joined together: a tent is a cylinder wearing a cone, a toy is a hemisphere under a cone, a pencil is a cylinder with a cone sharpened onto it. Volumes simply add, but surface areas do not, because the joined faces disappear inside; deciding which surfaces survive is most of the thinking. Melting and recasting questions rest on one fact only, that the volume does not change.
Work through these
For several combined solids, list which surfaces are exposed before computing anything
The listing is where combined-solid questions are won or lost: a flat top counted twice, a buried circle counted at all. Making it a written step rather than a mental one is what makes the errors visible.
Compute volumes of combined solids by plain addition of the parts
Volume is the forgiving half of the chapter, and doing it after the surface-area listing shows the contrast: nothing disappears inside. The practice consolidates the individual formulas at the same time.
Solve two melting-and-recasting problems by equating volumes before and after
A sphere recast as wire, a cone of scoops from a cylinder of ice cream: one equation, volume equals volume, carries every such question. Writing that equation first keeps the unknown from getting lost in the substitution.
Check one answer's units and size against the object it describes
Volumes in this chapter come out in thousands easily, and a slip of one power of ten hides well in them. Asking whether the number could be true of the actual tent or toy is the fastest audit there is.
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