Volume with Fractional Edges — Drills
Volume with Fractional Edges has 5 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 8 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.
- Volume — Space inside, in cubic units.
- Base — The number being multiplied. In 53 the base is 5.
- Dimensions — Rows × columns. A 2 × 3 matrix has two rows and three columns.
- Mixed number — A whole number with a fraction, like 212.
- Height — The perpendicular distance from the base to the opposite corner.
- Cubic unit — A cube one unit on every edge.
- Edge length — The measurement along one side.
Box
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the volume of a box 4 by 10 by 8.
Worked answer
320
4 × 10 = 40 on the bottom
40 × 8 = 320
Problem 2
Find the volume of a box 7 by 8 by 2.
Worked answer
112
7 × 8 = 56 on the bottom
56 × 2 = 112
Cubes
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the volume of a cube with edge 9.
Worked answer
729
93 = 729
Problem 2
Find the volume of a cube with edge 3.
Worked answer
27
33 = 27
Smallcubes
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A box holds exactly 320 cubes with 14-unit edges. Find its volume in cubic units.
Worked answer
5
14 × 14 × 14 = 164
320 ÷ 64 = 5
Problem 2
A box holds exactly 32 cubes with 12-unit edges. Find its volume in cubic units.
Worked answer
4
12 × 12 × 12 = 18
32 ÷ 8 = 4
Howmany
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
How many cubes with 15-inch edges fill one cubic inch?
Worked answer
125
5 × 5 × 5 = 125
Problem 2
How many cubes with 12-inch edges fill one cubic inch?
Worked answer
8
2 × 2 × 2 = 8
Working backwards
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A box has volume 126 with a base 3 by 6. Find its height.
Worked answer
7
Base area = 18
126 ÷ 18 = 7
Problem 2
A box has volume 75 with a base 5 by 5. Find its height.
Worked answer
3
Base area = 25
75 ÷ 25 = 3