Depth · one concept from first principles · step 2 of 4

For equal thickness the material ratio is the area ratio

Making a round pizza with a diameter of $10\ \text{cm}$ takes $25\ \text{g}$ of flour. How many grams of flour are needed to make a pizza of the same thickness with a diameter of $20\ \text{cm}$ ?

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.

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

3STEP 3

Scale the flour by the same factor

Four times the area takes four times the flour.

25 × 4 = 100

Answer

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

Where next?

Another one like thissuggested

12 practice problems

Step back and solidifysuggested

One full roll moves it its own circumference A part's share of a circle is its central angle's share

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▶ Practice — 12 problems