SME
Grade 6 Math · Problem type
Volume of prisms with fractional edges
Use this for “A box is 2 1/2 by 1 1/2 by 2. What is its volume?”
Diagram
5 × 3 × 4 = 60 cubes with edge 1/2.
8 of them make one unit cube, so the volume is 60 ÷ 8 = 7 1/2 cubic units.
This is an example. Type your own values to start a new problem.
l
×
w
×
h
=
7
1
2
V
Half-unit cubes
worked out (not typed)
Formulas
(2
×
2
1
2
)
×
(2
×
1
1
2
)
×
(2
×
2)
=
60
Half-units along the length × along the width × along the height = half-unit cubes
60
÷
8
=
7
1
2
Half-unit cubes ÷ 8 = volume
Assumptions
•
A half-unit cube has edges of 1/2, so 8 of them make one unit cube.
•
Count the half-unit cubes along each edge: twice the length.
•
Edges in halves, up to 5 units.
Step-by-step
WE KNOW
Length: 2 1/2
Width: 1 1/2
Height: 2
FIND
half-unit cubes, volume in cubic units
Step 1 · Find half-unit cubes
(2
×
2
1
2
)
×
(2
×
1
1
2
)
×
(2
×
2)
=
?
Half-units along the length × along the width × along the height = half-unit cubes
Count the half-unit cubes along each edge, then multiply.
5 × 3 × 4 = 60
Half-unit cubes = 60
Step 2 · Find volume in cubic units
60 ÷ 8 = ?
Half-unit cubes ÷ 8 = volume
8 half-unit cubes fill one unit cube.
7
.
5
8
)
6
0
.
0
−
5
6
4
0
−
4
0
0
Volume
in
cubic
units
=
7
1
2
(the
same
as
2
1
2
×
1
1
2
×
2)
Check
Put the numbers back in. Both sides should match.
(2
×
2
1
2
)
×
(2
×
1
1
2
)
×
(2
×
2)
=
60
✓
7
1
2
×
8
=
60
✓
Topic check
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