The circle's area is what percentage of the square's?
A normal-level "Area" problem.When a question asks for a percentage, try writing the side as a letter. Common factors cancel, and the answer often turns out not to depend on size at all.
GivenA circle fits exactly inside a square of side 10 cm / π = 3.14
Hints
- The square's area is 10 × 10 = 100 cm². Straightforward.
- The circle fits exactly, so its diameter equals the side, 10 cm. The radius is half of that, 5 cm, giving 5 × 5 × 3.14 = 78.5 cm².
- The ratio is 78.5 ÷ 100 = 0.785, that is 78.5%. But do not stop here.
- Try a smaller square. Call the side □: the square is □ × □ and the circle is (□÷2) × (□÷2) × ' + pi + '. The □ cancels out, so the ratio does not depend on □ at all.
- Tidied up it is just 3.14 ÷ 4. Any circle snug inside a square covers 78.5% of it, always — which is why a square pizza box always wastes about 21.5% of its floor.
Answer 78.5%
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?