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How much wider is the big circle than the two small ones?

A normal-level "Area" problem.Double the length and the area quadruples; triple it and it goes up ninefold. The same reasoning settles the medium-versus-large pizza question.

GivenThe big circle's diameter is 12 cm; each small one is half that / π = 3.14

Area ★★★☆☆☆ How much wider is the big circle than the two small ones? 12cm 6cm

Hints

  1. A circle's area is "radius × radius × π". The big radius is 6 cm, the small one half of that, 3 cm.
  2. The big circle is 6 × 6 × 3.14 = 113.04 cm².
  3. Each small circle is 3 × 3 × 3.14 = 28.26 cm². The radius is halved, but the area is a quarter, not a half — because it is "half times half". This is where most people trip.
  4. You can check it in the picture: four small circles fit inside the big one — there are gaps, but by area it is exactly four. So one small circle is a quarter of the big one.
  5. Two small circles come to 28.26 × 2 = 56.52 cm². The difference is 113.04 − 56.52. Two small circles only make half the big one.

Answer 56.52cm²

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