Volume with Fractional Edges — Practice
Volume still counts cubes — but when the cubes are smaller than one unit, counting is not the whole answer.
What these questions 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.
Problem 1
Find the volume of a box 6 by 4 by 3.
Worked answer
72
72
Problem 2
Find the volume of a box 5 by 5 by 2.
Worked answer
50
50
Problem 3
Find the volume of a cube with edge 4.
Worked answer
64
43 = 64
Problem 4
Find the volume of a cube with edge 10.
Worked answer
1000
1000
Problem 5
Volume is measured in
- cubic units
- square units
- units
- degrees
Worked answer
cubic units
Cubic units
Problem 6
Find the volume of a box 12 by 34 by 2.
Worked answer
3/4
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Problem 7
Find the volume of a box 13 by 12 by 6.
Worked answer
1
16 × 6 = 1
Problem 8
A box holds exactly 48 cubes with 12-inch edges. Find its volume in cubic inches.
Worked answer
6
48 × 18 = 6
Problem 9
How many 12-inch cubes fill one cubic inch?
Worked answer
8
2 × 2 × 2 = 8
Problem 10
How many 13-inch cubes fill one cubic inch?
Worked answer
27
33 = 27
Problem 11
A box has volume 60 with a base 5 by 4. Find its height.
Worked answer
3
60 ÷ 20 = 3
Problem 12
Find the volume of a box 212 by 2 by 3.
Worked answer
15
52 × 2 × 3 = 15
Problem 13
A container has volume 2500 cm³. How many litres does it hold?
Worked answer
2.5
2500 ÷ 1000 = 2.5
Problem 14
A box holds 135 cubes with 13-inch edges. Find its volume in cubic inches.
Worked answer
5
135 ÷ 27 = 5
Problem 15
If every edge of a cube is halved, the volume becomes
- one eighth
- one half
- one quarter
- one sixteenth
Worked answer
one eighth
12 × 12 × 12 = 18
Problem 16
A cube has volume 125 cm³. Find its edge length.
Worked answer
5
53 = 125