Solid Geometry (Standard)

Multi-step exam-style items.

Phase 2 · Gaokao

Solid Geometry: core idea

V=\pi r^2 h

Cylinder $r=3$ , $h=7$ : lateral area $/\pi$ ?

Hint: $2rh$ . Answer: 42.

1. Cone $r=6$ , $h=8$ : slant height?
2. Sphere $r=4$ : surface $/\pi$ ?
3. Prism $3\times4\times12$ : long space diagonal?
4. Angle line to plane: if direction makes $30^\circ$ with normal, angle with plane?
5. Distance point to plane $x=0$ from $(5,1,1)$ ?
6. Section cube edge $2$ midplane parallel face: area?
7. Regular tetrahedron edge $2$ : height $\dfrac{\sqrt6}{3}\cdot2$ : enter $\sqrt6$ coefficient as fraction $a/b$ : $a+b$ ?
8. Projection of length $10$ at $60^\circ$ : projected length?
9. Frustum — skip. Sphere diam $10$ : volume $/\pi$ ?