Volume & Surface Area of 3-D Figures — Practice
Volume fills the inside — base area times height. Surface area wraps the outside — add up every face.
What these questions cover
These questions use 15 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.
- π — The circumference of any circle divided by its diameter — about 3.14159.
- 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.
- Radius — Centre to edge. Half the diameter.
- 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.
- Dimensions — Rows × columns. A 2 × 3 matrix has two rows and three columns.
- Height — The perpendicular distance from the base to the opposite corner.
- Rectangular prism — A box — six rectangular faces meeting at right angles.
- Edge length — The measurement along one side.
Problem 1
Find the volume of a 5 × 4 × 3 rectangular prism.
Worked answer
60
5 × 4 × 3 = 60
Problem 2
Find the volume of a cube with edge 4 cm.
Worked answer
64
43 = 64 cm3
Problem 3
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 4
Find the surface area of a cube with edge 3.
Worked answer
54
One face: 3 × 3 = 9
6 × 9 = 54
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 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 9
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 10
A tank holds 1,680 cm3. Its base is 14 cm by 10 cm. How deep is it?
Worked answer
12
B = 140 cm2
1680 ÷ 140 = 12 cm
Problem 11
A cone and a cylinder have the same base and height. The cone holds what fraction of the cylinder?
- 12
- 13
- 23
- 14
Worked answer
13
Vcone = 13Bh, so it holds one third.
Problem 12
How many 2 cm cubes fit inside an 8 × 6 × 4 cm box?
Worked answer
24
Along each edge: 4, 3, 2
4 × 3 × 2 = 24 cubes
Check: 192 ÷ 8 = 24 ✓
Problem 13
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 14
A cylinder has volume 100π and radius 5. Find its height.
Worked answer
4
25π h = 100π
h = 4
Problem 15
A prism's base is a trapezoid with parallel sides 5 and 9 and height 4. The prism is 10 long. Find its volume.
Worked answer
280
B = 5 + 92 × 4 = 28
V = 28 × 10 = 280
Problem 16
A cube's edge is doubled. Its volume is multiplied by what?
Worked answer
8
2 × 2 × 2 = 8
A 3-cube holds 27; a 6-cube holds 216, which is 8 times as much.