Practice with lines and planes in space
Answers are for parents and teachers.
1
A cube has edge 8 cm. Find the area of the section through A, C and B₁.
32√3 cm²
2
Find the space diagonal of a rectangular parallelepiped with edges 6, 8 and 24.
26
3
A cube has edge 2 cm; find the area of triangle MNL formed by the midpoints of AB, BC and BB₁.
√3/2 cm²
4
Why does a three-legged support not wobble even on uneven ground, while a four-legged one might?
Three points not on one line determine exactly one plane, and the support rests on it; a fourth point need not lie in that plane.
5
How many edges of a cube are parallel to a given edge (not counting itself)?
3