Volume — Grade 7 Accelerated, what it means and where it is taught
Space inside, in cubic units.
Taught in Grade 7 Accelerated.
Where it is taught
What uses it later
This idea is needed for:
- Cavalieri's principle — Same height and same cross sections at every level means same volume.
Practise this idea
54 questions in the course bank use Volume, in Proportional Reasoning with Scale Drawings, Volume & Surface Area of 3-D Figures, Dilations & Similarity, Volume of Cylinders, Cones & Spheres, Systems of Equations & Inequalities, Similarity & Proportionality. The first 8 are below; the rest are in those units.
Problem 1
A cube's edge is tripled. Its volume is multiplied by what?
Worked answer
27
k3 = 33 = 27
A 2-cube holds 8; a 6-cube holds 216, which is 27 times as much.
Problem 2
Find the volume of a 5 × 4 × 3 rectangular prism.
Worked answer
60
5 × 4 × 3 = 60
Problem 3
Find the volume of a cube with edge 4 cm.
Worked answer
64
43 = 64 cm3
Problem 4
Find the volume of a cylinder with radius 2 and height 5. Use π ≈ 3.14.
Worked answer
62.8
π r2 = 3.14 × 4 = 12.56
12.56 × 5 = 62.8
Problem 5
A prism has base area 12 cm2 and height 10 cm. Find its volume.
Worked answer
120
12 × 10 = 120 cm3
Problem 6
A triangular prism has a base triangle with base 6 cm and height 4 cm, and the prism is 10 cm long. Find its volume.
Worked answer
120
B = 12(6)(4) = 12 cm2
V = 12 × 10 = 120 cm3
Problem 7
A cylinder has radius 3 and height 8. Find its volume in terms of π (enter just the number in front of π).
Worked answer
72
9 × 8 = 72
V = 72π
Problem 8
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.