Revision sheet

Cross sections and rotations

Parallel slices copy the base; rectangle → cylinder, right triangle → cone, semicircle → sphere.

Watch out: the angle of the slice decides the shape.

Scaling solids

Length $k$, area $k^2$, volume $k^3$.

Watch out: cube roots undo volume ratios.

Spheres and density

$V = \tfrac{4}{3}\pi r^3$; density = mass/volume.

Watch out: $r^3$ for volume, $r^2$ for area.

Converting units

To a smaller unit: multiply; to a larger unit: divide.

Watch out: check that the answer makes sense in size.