Depth · one concept from first principles · step 2 of 4
Scaling every edge by ■ scales volume by ■ cubed
Every edge of a cube is doubled. We need how many times bigger the new cube's volume is.
Geometry
Your answer
How to solve
Strategy Solve an Easier Related Problem — The answer is easiest to see with actual numbers first, then to explain with the three directions. A cube grows in three directions at once, so doubling each one multiplies the volume three times over.
1STEP 1
Work out both volumes
The new cube has edges 5 × 2 = 10 cm, and a cube's volume is its edge multiplied by itself three times.
5 × 5 × 5 = 125, 10 × 10 × 10 = 1000
125 cm³ becomes 1000 cm³.
6.G.A.2Draw A Diagram2STEP 2
Compare them
Divide the new volume by the old one.
1000 ÷ 125 = 8
The volume is 8 times as big.
6.RP.A.3Solve An Easier Related Problem3STEP 3
See why it is 8 and not 2
Length, depth and height each double, and volume is all three multiplied, so the doubling happens three times over.
2 × 2 × 2 = 8
Any cube would give 8, not just this one.
6.G.A.2Look For A PatternDoubling every edge multiplies the volume by .
Why?
A cube's volume counts unit cubes as rows within layers, so it is the three edge counts multiplied together.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
Doubling an edge doubles its count, and doubling all three doubles the product three separate times.
🧱Associativity of multiplicationMultiplying three numbers, grouping any two first gives the same product.
Answer
8 times
Stack it up: eight 5 cm cubes, two along each direction, build exactly the 10 cm cube.
Takeaway
Volume grows in three directions at once, so doubling every edge multiplies it by 2 × 2 × 2.
- Work out both volumes
- Compare them
- See why it is 8 and not 2
Where next?
Another one like thissuggested
Step back and solidifysuggested
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