Volume & Surface Area of 3-D Figures — Drills
Volume & Surface Area of 3-D Figures has 6 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 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.
Prism
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the volume of a 6 × 7 × 9 rectangular prism.
Worked answer
378
6 × 7 × 9 = 378
Problem 2
Find the volume of a 8 × 6 × 5 rectangular prism.
Worked answer
240
8 × 6 × 5 = 240
Cylinder
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A cylinder has radius 5 and height 8. Find its volume in terms of π (enter just the number in front of π).
Worked answer
200
r2 = 25
25 × 8 = 200
V = 200π
Problem 2
A cylinder has radius 6 and height 7. Find its volume in terms of π (enter just the number in front of π).
Worked answer
252
r2 = 36
36 × 7 = 252
V = 252π
Surface
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the surface area of a 8 × 6 × 4 rectangular prism.
Worked answer
208
2(8 × 6) = 96
2(8 × 4) = 64
2(6 × 4) = 48
96 + 64 + 48 = 208
Problem 2
Find the surface area of a 2 × 5 × 8 rectangular prism.
Worked answer
132
2(2 × 5) = 20
2(2 × 8) = 32
2(5 × 8) = 80
20 + 32 + 80 = 132
Working backwards
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A tank holds 450 cm3. Its base is 5 cm by 9 cm. How deep is it?
Worked answer
10
B = 5 × 9 = 45 cm2
450 ÷ 45 = 10 cm
Problem 2
A tank holds 147 cm3. Its base is 7 cm by 7 cm. How deep is it?
Worked answer
3
B = 7 × 7 = 49 cm2
147 ÷ 49 = 3 cm
Pyramid
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A pyramid has base area 48 and height 9. Find its volume.
Worked answer
144
V = 13Bh
= 13 × 48 × 9 = 144
Problem 2
A pyramid has base area 12 and height 6. Find its volume.
Worked answer
24
V = 13Bh
= 13 × 12 × 6 = 24
Scaling
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A cube has edge 4. If the edge is multiplied by 4, how many times larger is the new volume?
Worked answer
64
Old volume: 43 = 64
New edge 16, new volume 4096
4096 ÷ 64 = 64
Problem 2
A cube has edge 3. If the edge is multiplied by 2, how many times larger is the new volume?
Worked answer
8
Old volume: 33 = 27
New edge 6, new volume 216
216 ÷ 27 = 8