Surface area — Grade 7 Accelerated, what it means and where it is taught
Total area of all the outside faces, in square units.
Taught in Grade 7 Accelerated.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Area — Space inside, measured in square units.
Practise this idea
20 questions in the course bank use Surface area, in Volume & Surface Area of 3-D Figures, Solids: Volume, Sections & Rotations, Surface Area & Nets. The first 8 are below; the rest are in those units.
Problem 1
Find the surface area of a cube with edge 3.
Worked answer
54
One face: 3 × 3 = 9
6 × 9 = 54
Problem 2
A cylinder has radius 3 and height 8. Find its surface area in terms of π (enter just the number in front of π).
Worked answer
66
Two circles: 2π(9) = 18π
Label: 2π(3)(8) = 48π
18 + 48 = 66, so SA = 66π
Problem 3
Find the surface area of a 5 × 4 × 3 rectangular prism.
Worked answer
94
2(5 × 4) = 40
2(5 × 3) = 30
2(4 × 3) = 24
40 + 30 + 24 = 94
Problem 4
A cube has volume 216 cm3. Find its surface area.
Worked answer
216
63 = 216, so the edge is 6 cm
SA = 6 × 62 = 6 × 36 = 216 cm2
The numbers match here by coincidence — the units do not.
Problem 5
A cone has r = 5 and ℓ = 13. Find its total surface area in terms of π.
Worked answer
90pi
Lateral = π r ℓ = 65π
Base = 25π
Total = 90π
Problem 6
Find the surface area of a sphere with r = 6, in terms of π.
Worked answer
144pi
4π(36) = 144π
Problem 7
Find the surface area of a box 5 by 3 by 4.
Worked answer
94
15+20+12 = 47
× 2 = 94
Problem 8
Find the surface area of a cube with edge 7.
Worked answer
294
6 × 49 = 294