Plane Sections of 3-D Figures — Drills
Plane Sections of 3-D Figures has 4 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 17 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Area — Space inside, measured in square units.
- Cross section — The 2-D face revealed when a plane cuts through a solid.
- Plane — A perfectly flat surface extending forever.
- Net — A 3-D shape unfolded flat.
- Face — A flat surface; a line where two faces meet; a corner point.
- Edge — A flat surface; a line where two faces meet; a corner point.
- Base — The number being multiplied. In 53 the base is 5.
- Radius — Centre to edge. Half the diameter.
- Diameter — All the way across through the centre. d = 2r.
- Cylinder — Two parallel circles joined by a curved surface. V = π r2 h.
- Cone — A circle tapering to a point. V = 13π r2 h.
- Parallel — Same slope, different intercept.
- Trapezoid — A quadrilateral with exactly one pair of parallel sides.
- Diagonal — A segment joining two non-adjacent vertices.
- Pyramid — A base tapering to a point. V = 13 Bh.
- Height — The perpendicular distance from the base to the opposite corner.
- Rectangular prism — A box — six rectangular faces meeting at right angles.
Slice
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A square pyramid is sliced parallel to its base. What shape is the cross section?
- A triangle
- A square
- A pentagon
- A trapezoid
Worked answer
A square
Parallel cuts copy the base shape — smaller the higher you cut.
Problem 2
A single flat cut slices off one corner of a cube. What shape is the new face?
- A triangle
- A hexagon
- A square
- A pentagon
Worked answer
A triangle
Three faces meet at a corner, so the plane crosses three faces — a triangle.
Solids
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
How many vertices does a cube have?
Worked answer
8
Four corners on top, four below.
Answer: 8
Problem 2
How many faces does a triangular prism have?
Worked answer
5
Two triangles plus three rectangles.
Answer: 5
Measure
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A cylinder has radius 8 cm and height 10 cm. It is cut vertically through its axis. Find the area of the cross section.
Worked answer
160
Height = 10 cm
Width = 2 × 8 = 16 cm
10 × 16 = 160 cm2
Problem 2
A cylinder has radius 2 cm and height 9 cm. It is cut vertically through its axis. Find the area of the cross section.
Worked answer
36
Height = 9 cm
Width = 2 × 2 = 4 cm
9 × 4 = 36 cm2
Nets
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
How many distinct nets can fold into a cube?
- 14
- 6
- 11
- 8
Worked answer
11
There are exactly 11.
Six have a row of four squares; the rest use rows of three or a staircase.
Problem 2
A cube net is a row of four squares A, B, C, D, with E above B and F below B. Which face ends up opposite A?
- B
- C
- E
- D
Worked answer
C
In a row of four, faces two apart end up opposite each other.
So A is opposite C, B opposite D, and E opposite F.