Learning goals
- The inscribed circle has area π · 4² ≈ 50.27 — about 78.5% of the square.
- No matter the square size, the inscribed circle always covers π/4 ≈ 78.5% — a constant ratio.
- The four leftover corners total 64 − 16π ≈ 13.73 cm².
Square Minus Inscribed Circle
Compute the four corner gaps
A square with the largest possible circle carved out. Change the side length and watch the four corner gaps scale together.
What this game shows · Square with Inscribed Circle
Carve the biggest possible circle out of a square and four corner gaps remain. The circle's area is always π/4 ≈ 78.5% of the square — the same constant ratio for any side length.
- Inscribed circle
- the largest circle that fits inside the square.
- Diameter = side
- the inscribed circle's diameter equals the square's side.
- Constant ratio
- circle / square = πr² / (2r)² = π/4.
Aligned with CCSS 7.G.B.4.
Inscribed circle
The largest circle in a square always covers pi over four of the square.
13.73
Side 8, circle radius 4.
Geometry and measurement model
Who this demo helps, and where to practice next
Square Minus Inscribed Circle is built for students who memorize formulas before seeing the shape decomposition. It gives the page a clear search purpose: learn the model, manipulate it, then continue into the matching grade-level practice.
Square Minus Inscribed Circle helps when a student can copy a procedure but cannot explain why it works. The demo slows the idea down into a visible model before sending the learner to guided missions.
How to play
- 1 Identify the shape pieces before calculating.
- 2 Drag or replay the model until the formula can be described from the picture.
- 3 Open the related geometry topic when the student can explain area, perimeter, or surface area in units.
Continue with guided practice
FAQ
Tap to expand Inscribed circle, in a square.
01 Why does the inscribed circle always cover ~78.5% of the square? π/4
Circle / square = πr² / (2r)² = π / 4 ≈ 0.785. The size of the square cancels out — the ratio is a universal constant.
02 For an 8 × 8 square, what are the four corner gaps? ~13.73
Total leftover = 64 − 16π ≈ 13.73 cm². Divided into four equal corner pieces, each is about 3.43 cm².
03 How does this relate to π itself? Estimating π
The ratio circle/square is π/4. Four times the experimental ratio gives an estimate of π — a low-tech experimental approach to estimating π.
04 Which grade is this game for? Grades 6–7
Grades 6–7, aligned with CCSS 7.G.B.4. Same composite-figure family as Four Quarter-Circles.