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
Hints
- A circle's area is "radius × radius × π". The big radius is 6 cm, the small one half of that, 3 cm.
- The big circle is 6 × 6 × 3.14 = 113.04 cm².
- 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.
- 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.
- 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
More "Area" problems
- Area of the inner triangle?
- Area of triangle DOA?
- Area of quadrilateral ABCD?
- Area of the overlap?
- Total area of the two crescents?
- Area swept by the square?
Browse by idea
- Ratios — answers without fixing a single number
- Circles and sectors — multiply by π once, at the very end