SME
Grade 5 Math · Problem type
Combine volumes of prisms
Use this for “Two stacks of cubes side by side, both 3 cubes deep. How many cubes in all?”
Diagram
First box: 4 × 3 × 2 = 24 cubes.
Second box: 2 × 3 × 5 = 30 cubes.
Together: 24 + 30 = 54 cubes.
This is an example. Type your own values to start a new problem.
First length
×
Width of both
×
First height
+
Second length
×
Width of both
×
Second height
=
Total volume
First volume
worked out (not typed) · cubic units
Second volume
worked out (not typed) · cubic units
Formulas
4 × 3 × 2 = 24
First length × width × first height = first volume
2 × 3 × 5 = 30
Second length × width × second height = second volume
3 × (4 × 2 + 2 × 5) = 54
Width × (first front + second front) = total volume
24 + 30 = 54
First volume + second volume = total volume
Assumptions
•
Split the shape into two boxes that do not overlap.
•
Find each box’s volume: length × width × height. Add the two.
•
Here both boxes are the same width. Count in unit cubes; sides to 6.
Step-by-step
WE KNOW
Width of both: 3 units
First length: 4 units
First height: 2 units
Second length: 2 units
Second height: 5 units
FIND
first volume, second volume, total volume
Step 1 · Find first volume
4 × 3 × 2 = ?
First length × width × first height = first volume
Length × width is the cubes in one layer. Times the height: all the layers.
4 × 3 = 12
12 × 2 = 24
First volume = 24 cubic units
Step 2 · Find second volume
2 × 3 × 5 = ?
Second length × width × second height = second volume
Length × width is the cubes in one layer. Times the height: all the layers.
2 × 3 = 6
6 × 5 = 30
Second volume = 30 cubic units
Step 3 · Find total volume
24 + 30 = ?
First volume + second volume = total volume
Add the two volumes.
Total volume = 54 cubic units
Check
Put the numbers back in. Both sides should match.
4 × 3 × 2 = 24 ✓
2 × 3 × 5 = 30 ✓
3 × (4 × 2 + 2 × 5) = 54 ✓
24 + 30 = 54 ✓
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Volume of rectangular prisms (length × width × height)
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Convert units of measure with decimals
Topic check
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