SME
Grade 8 Math · Problem type
Cube roots as edges
Use this for “A cube has volume 1,000 cm³. What is its edge?”
Diagram
A cube of volume 1,000 has edge ∛1,000 = 10
10³ = 1,000
This is an example. Type your own values to start a new problem.
V
Volume of the cube
example · cm³
e
Edge
calculated · cm
Formulas
e
=
∛
V
(edge
=
∛volume
of
the
cube)
10 = ∛1,000
Assumptions
•
A cube of volume V has edge ∛V, because edge × edge × edge = volume.
•
If V is a perfect cube (8, 27, 64, …), the edge is a whole number.
•
If not, the edge lies between two whole numbers whose cubes are on either side of V.
Step-by-step
WE KNOW
V = 1,000 cm³ (volume of the cube)
FIND
edge (e)
Step 1 · Find edge (e)
Use e = ∛V (edge = ∛volume of the cube)
The edge is the number that, used as a factor three times, makes the volume.
e
=
∛1,000
e
=
10
cm
Check
Put the numbers back in. Both sides should match.
10 = ∛1,000 ✓
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