SME
Grade 6 Math · Problem type
Surface area and volume of cubes
Use this for “What is the volume and surface area of a cube with side 2?”
Diagram
Six faces add to 54 square units.
This is an example. Type your own values to start a new problem.
V
=
s
3
SA
=
6
×
s
2
Formulas
V
=
s
3
(volume
=
edge
×
edge
×
edge)
27
=
3
3
SA
=
6
×
s
2
(surface
area
=
6
faces
×
edge
×
edge)
54
=
6
×
3
2
Assumptions
•
s³ means s × s × s; s² means s × s.
•
A cube has 6 square faces, each s × s.
•
Edges are whole numbers to 20 units; volume is in cubic units, surface area in square units.
Step-by-step
WE KNOW
s = 3 units (edge)
FIND
volume (V), surface area (SA)
Step 1 · Find volume (V)
Use V = s³ (volume = edge × edge × edge)
Use the edge as a factor three times.
3
3
=
3
×
3
×
3
V
=
27
cubic
units
Step 2 · Find surface area (SA)
Use SA = 6 × s² (surface area = 6 faces × edge × edge)
Square the edge for one face, then multiply by 6 faces.
SA
=
6
×
3
2
3
2
=
9
6 × 9 = 54
SA = 54 square units
Check
Put the numbers back in. Both sides should match.
27
=
3
3
✓
54
=
6
×
3
2
✓
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