Surface Area & Nets — Drills
Surface Area & Nets 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 12 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Perimeter — Distance all the way around the outside.
- Area — Space inside, measured in square units.
- Face — A flat surface; a line where two faces meet; a corner point.
- Volume — Space inside, in cubic units.
- Surface area — Total area of all the outside faces, in square units.
- Prism — A solid with two identical parallel bases joined by rectangles.
- Base — The number being multiplied. In 53 the base is 5.
- Square root — For k ≥ 0, √k is the nonnegative number whose square is k.
- Pyramid — A base tapering to a point. V = 13 Bh.
- Height — The perpendicular distance from the base to the opposite corner.
- Cubic unit — A cube one unit on every edge.
- Capacity — How much a container holds, often in litres or gallons.
Box
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the surface area of a box 4 by 10 by 8.
Worked answer
304
40 + 32 + 80 = 152
× 2 = 304
Problem 2
Find the surface area of a box 7 by 8 by 2.
Worked answer
172
56 + 14 + 16 = 86
× 2 = 172
Cubes
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the surface area of a cube with edge 11.
Worked answer
726
Each face is 121
6 × 121 = 726
Not 1331 — that would be the volume
Problem 2
Find the surface area of a cube with edge 3.
Worked answer
54
Each face is 9
6 × 9 = 54
Not 27 — that would be the volume
Pyramid
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A square pyramid has base edge 12 and slant height 10. Find its surface area.
Worked answer
384
Base = 144
Each triangle = 12 × 12 × 10 = 60
144 + 4(60) = 384
Problem 2
A square pyramid has base edge 4 and slant height 8. Find its surface area.
Worked answer
80
Base = 16
Each triangle = 12 × 4 × 8 = 16
16 + 4(16) = 80
Working backwards
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A cube has surface area 54. Find the length of one edge.
Worked answer
3
54 ÷ 6 = 9
√9 = 3
Problem 2
A cube has surface area 150. Find the length of one edge.
Worked answer
5
150 ÷ 6 = 25
√25 = 5