Problem
For equal thickness the material ratio is the area ratio
A larger pizza of the same thickness is to be made. We need how much flour it takes.
GeometryRatios
Your answer
How to solve
Strategy Solve an Easier Related Problem — The tempting answer is to double the flour because the diameter doubled, but flour fills a surface. Compare the two areas and the true factor appears -- and the two circle areas are easier to compare than to compute.
1STEP 1
See what the flour goes with
The pizzas are equally thick, so the flour is spread over the round face -- twice the area needs twice the flour.
Flour follows area, not diameter.
7.RP.A.2Solve An Easier Related ProblemThe flour goes with the pizza's area, not its diameter.
Why?
Both pizzas are the same thickness, so the dough is spread in a layer of one fixed depth and every equal patch of area takes the same flour.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
The whole pizza is made of those equal patches with none left over, so the flour adds up to the area's worth.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
2STEP 2
Compare the two areas
Radii of 5 and 10 cm give areas of 78.5 and 314 cm².
5 × 5 × 3.14 = 78.5, 10 × 10 × 3.14 = 314
The big one is four times the small one.
7.G.B.4Draw A Diagram3STEP 3
Scale the flour by the same factor
Four times the area takes four times the flour.
25 × 4 = 100
The big pizza takes 100 g of flour.
7.RP.A.2Identify SubproblemsAnswer
100 g
Check the factor without the numbers: doubling the radius doubles it in both directions of the multiplication, so the area is 2 × 2 = 4 times as big.
Takeaway
Doubling a circle's diameter makes it four times the area, not twice.
- See what the flour goes with
- Compare the two areas
- Scale the flour by the same factor