Surface Area & Nets — Practice
Unfold a solid and its surface becomes a flat shape whose area you already know how to find.
What these questions 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.
Problem 1
Find the surface area of a box 5 by 3 by 4.
Worked answer
94
15+20+12 = 47
× 2 = 94
Problem 2
Find the surface area of a cube with edge 7.
Worked answer
294
6 × 49 = 294
Problem 3
Find the surface area of a cube with edge 3.
Worked answer
54
54
Problem 4
How many faces does a rectangular box have?
Worked answer
6
Six
Problem 5
How many faces does a square pyramid have?
Worked answer
5
One square and four triangles
Problem 6
Find the surface area of a box 2 by 6 by 10.
Worked answer
184
12+20+60 = 92
× 2 = 184
Problem 7
A square pyramid has base edge 6 and slant height 5. Find its surface area.
Worked answer
96
36 + 4(15) = 96
Problem 8
A square pyramid has base edge 10 and slant height 12. Find its surface area.
Worked answer
340
100 + 4(60) = 340
Problem 9
Surface area is measured in
- square units
- cubic units
- units
- no units
Worked answer
square units
Squared units
Problem 10
A triangular prism has two triangular ends of area 6 each and three rectangles of areas 20, 15 and 25. Find the surface area.
Worked answer
72
12 + 60 = 72
Problem 11
A cube has surface area 150. Find the length of one edge.
Worked answer
5
150 ÷ 6 = 25
√25 = 5
Problem 12
A box is 4 by 4 by 9. Find its surface area.
Worked answer
176
16+36+36 = 88
× 2 = 176
Problem 13
How much paper is needed to wrap a box 8 by 6 by 2, with no overlap?
Worked answer
152
48+16+12 = 76
× 2 = 152
Problem 14
Which do you need to work out how much paint covers a box?
- Surface area
- Volume
- Perimeter
- Capacity
Worked answer
Surface area
Covering is area
Problem 15
A cube has edge 2.5 cm. Find its surface area in cm².
Worked answer
37.5
6 × 6.25 = 37.5
Problem 16
A prism has an end of area 14 and length 9, with the wrapping area 9 times the perimeter 18. Find the total surface area.
Worked answer
190
2(14) = 28
18 × 9 = 162
28+162 = 190